library(readr)
## Warning: package 'readr' was built under R version 4.2.2
train <- read_csv("C:/Users/vidhi/Downloads/train.csv")
## Rows: 891 Columns: 11
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): Name, Sex, Ticket, Embarked
## dbl (7): PassengerId, Survived, Pclass, Age, SibSp, Parch, Fare
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
View(train)
str(train)
## spc_tbl_ [891 × 11] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ PassengerId: num [1:891] 1 2 3 4 5 6 7 8 9 10 ...
## $ Survived : num [1:891] 0 1 1 1 0 0 0 0 1 1 ...
## $ Pclass : num [1:891] 3 1 3 1 3 3 1 3 3 2 ...
## $ Name : chr [1:891] "Braund, Mr. Owen Harris" "Cumings, Mrs. John Bradley (Florence Briggs Thayer)" "Heikkinen, Miss. Laina" "Futrelle, Mrs. Jacques Heath (Lily May Peel)" ...
## $ Sex : chr [1:891] "male" "female" "female" "female" ...
## $ Age : num [1:891] 22 38 26 35 35 NA 54 2 27 14 ...
## $ SibSp : num [1:891] 1 1 0 1 0 0 0 3 0 1 ...
## $ Parch : num [1:891] 0 0 0 0 0 0 0 1 2 0 ...
## $ Ticket : chr [1:891] "A/5 21171" "PC 17599" "STON/O2. 3101282" "113803" ...
## $ Fare : num [1:891] 7.25 71.28 7.92 53.1 8.05 ...
## $ Embarked : chr [1:891] "S" "C" "S" "S" ...
## - attr(*, "spec")=
## .. cols(
## .. PassengerId = col_double(),
## .. Survived = col_double(),
## .. Pclass = col_double(),
## .. Name = col_character(),
## .. Sex = col_character(),
## .. Age = col_double(),
## .. SibSp = col_double(),
## .. Parch = col_double(),
## .. Ticket = col_character(),
## .. Fare = col_double(),
## .. Embarked = col_character()
## .. )
## - attr(*, "problems")=<externalptr>
attach(train)
#Get the Correlations between the measurements
Temp2=train[,-c(1,3,4,7,8,9)]
Temp2=na.omit(Temp2)
Temp2$Sex<-as.numeric(factor(Temp2$Sex, levels = unique(Temp2$Sex)))
Temp2$Embarked<-as.numeric(factor(Temp2$Embarked, labels=c("1","2","3")))
cor(Temp2[-1])
## Sex Age Fare Embarked
## Sex 1.00000000 -0.09903723 0.18245683 -0.10963900
## Age -0.09903723 1.00000000 0.09314252 -0.03256492
## Fare 0.18245683 0.09314252 1.00000000 -0.28351044
## Embarked -0.10963900 -0.03256492 -0.28351044 1.00000000
# Using prcomp to compute the principal components (eigenvalues and eigenvectors). With scale=TRUE, variable means are set to zero, and variances set to one
Temp2_pca <- prcomp(Temp2[,-1],scale=TRUE)
Temp2_pca
## Standard deviations (1, .., p=4):
## [1] 1.1816256 1.0408997 0.9141950 0.8273671
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Sex 0.44571001 -0.5293273 0.64187639 0.3303784
## Age 0.09242234 0.8292140 0.48163361 0.2681255
## Fare 0.65697225 0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
summary(Temp2_pca)
## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion 0.3491 0.6199 0.8289 1.0000
# sample scores stored in Temp2_pca$x
# singular values (square roots of eigenvalues) stored in sparrow_pca$sdev
# loadings (eigenvectors) are stored in Temp2_pca$rotation
# variable means stored in Temp2_pca$center
# variable standard deviations stored in Temp2_pca$scale
# A table containing eigenvalues and %'s accounted, follows
# Eigenvalues are sdev^2
(eigen_Temp2 <- Temp2_pca$sdev^2)
## [1] 1.3962390 1.0834721 0.8357525 0.6845364
names(eigen_Temp2) <- paste("PC",1:4,sep="")
eigen_Temp2
## PC1 PC2 PC3 PC4
## 1.3962390 1.0834721 0.8357525 0.6845364
sumlambdas <- sum(eigen_Temp2)
sumlambdas
## [1] 4
propvar <- eigen_Temp2/sumlambdas
propvar
## PC1 PC2 PC3 PC4
## 0.3490598 0.2708680 0.2089381 0.1711341
cumvar_Temp2 <- cumsum(propvar)
cumvar_Temp2
## PC1 PC2 PC3 PC4
## 0.3490598 0.6199278 0.8288659 1.0000000
matlambdas <- rbind(eigen_Temp2,propvar,cumvar_Temp2)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
## PC1 PC2 PC3 PC4
## Eigenvalues 1.3962 1.0835 0.8358 0.6845
## Prop. variance 0.3491 0.2709 0.2089 0.1711
## Cum. prop. variance 0.3491 0.6199 0.8289 1.0000
summary(Temp2_pca)
## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion 0.3491 0.6199 0.8289 1.0000
Temp2_pca$rotation
## PC1 PC2 PC3 PC4
## Sex 0.44571001 -0.5293273 0.64187639 0.3303784
## Age 0.09242234 0.8292140 0.48163361 0.2681255
## Fare 0.65697225 0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
print(Temp2_pca)
## Standard deviations (1, .., p=4):
## [1] 1.1816256 1.0408997 0.9141950 0.8273671
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Sex 0.44571001 -0.5293273 0.64187639 0.3303784
## Age 0.09242234 0.8292140 0.48163361 0.2681255
## Fare 0.65697225 0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
## Sample scores stored in sparrow_pca$x
Temp2_pca$x
## PC1 PC2 PC3 PC4
## [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [2,] 2.328844131 0.1022918285 -0.0644045317 1.147406212
## [3,] -0.076863406 -1.0364253330 1.0155382614 0.470315955
## [4,] 0.541154997 -0.4004517724 1.3498713191 0.005941459
## [5,] -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## [6,] -0.278861772 1.7828311382 0.6470218066 -0.311526470
## [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
## [8,] -0.030671121 -0.9706142289 1.0512734542 0.444011801
## [9,] 1.664344689 -1.3812908595 -0.8941309506 1.278937145
## [10,] -0.108260428 -2.2716456857 0.2912731112 -0.059238176
## [11,] 0.358340114 0.8443588327 2.0935020004 0.802227620
## [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
## [13,] -0.630009991 0.8694448494 0.1324763008 -0.301524135
## [14,] -0.154266787 -1.7231957561 0.6166953333 0.249299556
## [15,] 0.208282705 0.6444468869 1.9855747253 0.894059299
## [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
## [17,] 0.080053345 -0.7233559402 1.1895595915 0.422118607
## [18,] -0.720981351 0.6264512250 -0.0045681066 -0.301859366
## [19,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [20,] 0.625733012 -1.5243219921 -0.1140148752 0.935304605
## [21,] -0.647725138 0.2513992845 -0.2297830451 -0.564031854
## [22,] -0.028458129 -2.0310634439 0.4276154032 -0.046334256
## [23,] 0.290832573 -0.2869811981 1.4326297117 0.364662359
## [24,] 2.118171868 0.3460076983 -0.3513946758 -3.907620912
## [25,] 0.875161156 1.1995167387 -1.3652222002 1.106508508
## [26,] -0.715648479 2.3585887361 1.0135414535 0.488114652
## [27,] 1.474364633 0.6588246642 -1.7215319207 0.124097704
## [28,] -0.353680136 1.0966188162 0.2483413792 -0.535451822
## [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
## [30,] -0.002848466 -1.4671517284 0.7575395885 0.181613043
## [31,] 1.430674269 -1.4317399327 -0.9088200604 1.541889474
## [32,] 0.031651073 -0.2312615472 1.4819997708 0.707675872
## [33,] 0.091775301 -0.9441782404 1.0589707441 0.306221266
## [34,] 1.737017034 -1.9798219080 -1.2507083116 0.914715217
## [35,] 0.649379751 -1.2958636466 0.0187973373 1.011401099
## [36,] -0.005330479 -1.4676875913 0.7573835629 0.184406085
## [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
## [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
## [39,] 2.466575808 0.7462487722 0.3053993550 1.274857785
## [40,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [41,] 1.459736803 2.7216822690 -0.5076885621 1.090593468
## [42,] -0.076792792 -1.3156014023 0.8513855516 0.341853400
## [43,] 0.547522780 0.4866401084 -1.7633798140 1.179923077
## [44,] 0.035247891 -2.1848242042 0.3331258345 -0.195053315
## [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
## [46,] 0.506071875 0.1147422142 -1.9793898155 1.059670295
## [47,] 0.056057955 1.3525954097 0.3725928346 -0.919505513
## [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
## [49,] -0.025776293 -0.8578809172 1.1172440150 0.489856824
## [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
## [51,] -0.134256967 -1.5513608787 0.7164474901 0.303812103
## [52,] -0.993534474 0.0650630709 -0.3171843486 -0.226241395
## [53,] -0.932468599 0.4132766744 -0.1163570157 -0.140899900
## [54,] 0.343048387 -1.5041496720 0.7136206745 -0.258982373
## [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [56,] 0.621242869 0.3629605012 -1.8408241584 1.032773366
## [57,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [58,] -1.012476731 0.0051352047 -0.3512065362 -0.230602048
## [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
## [60,] 0.005110655 -0.7953742112 1.1520170759 0.480775963
## [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
## [62,] -0.964009855 0.2389521784 -0.2168340676 -0.182435974
## [63,] -0.503768344 0.2824793282 -0.2207335593 -0.726028287
## [64,] -0.102301041 -1.5444616449 0.7184563199 0.267851688
## [65,] 0.066125823 -0.6146863442 1.2543469319 0.489144664
## [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
## [67,] 3.069503611 -0.5246444689 1.1148325103 -3.147361192
## [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
## [69,] -0.982004454 0.2350671729 -0.2179652533 -0.162186420
## [70,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [71,] -0.214309508 1.3500617657 0.3884282861 -0.589580909
## [72,] -0.845699534 0.0969804002 -0.3078910727 -0.392601955
## [73,] -0.800620638 1.9493755407 0.7783798817 0.403998588
## [74,] 1.158894058 2.9917603749 -0.3296117147 1.583195391
## [75,] 1.209014909 0.3223447643 -1.9023696200 0.294316071
## [76,] 0.161234875 -0.5383141877 1.2931571557 0.407793843
## [77,] -0.727358414 0.5692361643 -0.0378004145 -0.320359794
## [78,] -0.064471655 -0.9220734477 1.0819800975 0.507724595
## [79,] -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
## [80,] -0.948998041 0.4655462570 -0.0845646682 -0.096622488
## [81,] -0.932539213 0.6924527437 0.0477956940 -0.012437345
## [82,] -0.990295149 0.1774389620 -0.2513178570 -0.178533413
## [83,] -0.112161487 -1.3232374475 0.8491621866 0.381654248
## [84,] -0.926524525 0.7495895684 0.0810052222 0.006470867
## [85,] -0.321794824 1.3826941194 0.4145029188 -0.442949682
## [86,] 1.473730145 -1.3945251058 -0.8896977450 1.506276452
## [87,] -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
## [88,] -0.091546650 -1.3746250000 0.8176266572 0.332779489
## [89,] 1.489723682 -1.2514764691 -0.8066137767 1.552470265
## [90,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [91,] 0.050371589 2.7498782185 0.3968624480 1.279719438
## [92,] -0.821294068 0.2697642906 -0.2078625945 -0.343035886
## [93,] 3.500861199 0.8729890093 -1.7254669726 -2.259051431
## [94,] 0.059862195 -2.3470248039 0.2361788623 -0.299781963
## [95,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [96,] 0.856496849 0.7767001720 -1.6126312086 0.934937055
## [97,] 0.027568597 -0.6509299197 1.2355074129 0.519695298
## [98,] 0.036664218 1.8509526994 0.6668565633 -0.666591926
## [99,] 0.492096651 -0.4466576443 -2.3085826307 0.818630611
## [100,] -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## [101,] -0.893312280 1.1476278804 0.3129130357 0.148833028
## [102,] 0.584492113 0.7458939120 -1.6133143950 1.253865794
## [103,] -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## [104,] 0.138651104 0.1827074307 1.7185460698 0.767003689
## [105,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [106,] -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## [107,] 0.609453478 0.1929004015 -1.9400595584 0.969010264
## [108,] 0.106324917 -1.3877431053 0.7972339315 0.084435450
## [109,] -0.371914372 0.8134907585 0.0830379805 -0.643315693
## [110,] -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## [111,] 1.411988553 0.4220047153 -1.8567787569 0.091583837
## [112,] -0.104543417 -1.2657544555 0.8824725073 0.398758155
## [113,] 0.008732262 -1.1296218900 0.9552561607 0.322640812
## [114,] -0.290457192 -0.1993767184 -1.3153815378 0.340912606
## [115,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [116,] -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## [117,] -0.997913218 0.1199559700 -0.2846281777 -0.195637320
## [118,] 0.142972844 -1.9382135057 0.4712234148 -0.213571117
## [119,] -0.711415758 0.7122738159 0.0452803553 -0.274108724
## [120,] -0.837672804 0.9921255660 0.2179163837 0.009191356
## [121,] -0.786174026 1.5057884376 0.5166365941 0.182328683
## [122,] 0.625789110 -1.1080768203 0.9283830454 -0.423094436
## [123,] -0.813012301 1.7512662798 0.6626909065 0.328074922
## [124,] -0.828623295 0.9103219462 0.1692381139 -0.039507101
## [125,] 1.363011889 1.9190638316 -0.9734089498 0.839966602
## [126,] 0.628437935 -1.4678997405 -0.0810134072 0.957937339
## [127,] -0.975627392 0.2922822335 -0.1847329454 -0.143685992
## [128,] -0.786447467 1.1148615610 0.2867993966 0.002900062
## [129,] 0.109524253 -0.2144488512 1.4868950745 0.620044181
## [130,] -1.004548410 0.0626851796 -0.3178767123 -0.213847271
## [131,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [132,] -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## [133,] -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## [134,] 0.292191896 0.1041801184 1.6625351704 0.542869023
## [135,] -0.387165823 0.3076536277 -0.2134036318 -0.857242604
## [136,] -0.462102217 2.1341376573 0.8653228600 0.074412689
## [137,] -0.108437846 -0.9976529748 -1.7964107906 -0.249065381
## [138,] -0.196474743 -2.4582058055 0.1872334484 -0.036999327
## [139,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [140,] 1.014114107 2.1229286683 -0.8311843925 1.360968857
## [141,] -1.054582031 -0.3948231038 -0.5836733895 -0.362956740
## [142,] 1.877062338 0.6748120111 0.3011724864 1.963921497
## [143,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [144,] -1.037266068 0.6140041188 0.0083808710 0.079736514
## [145,] -0.819925729 -0.8467055469 -0.8644051723 -0.858108061
## [146,] -0.776470582 -1.2840297533 -1.1243249106 -1.112421644
## [147,] -0.042176813 -2.2573783381 0.2954272933 -0.133602918
## [148,] -0.650385190 1.2000754541 0.3281840430 -0.124535951
## [149,] -0.047950783 1.0255835534 -0.6106769508 0.607226009
## [150,] -0.939278650 0.6351594471 0.0145406064 -0.030529989
## [151,] 0.024380066 -0.6795374501 1.2188912589 0.510445084
## [152,] -0.984345239 -0.3238208286 -0.5464266984 -0.416318488
## [153,] -0.122381475 -1.4371204529 0.7828568729 0.341801696
## [154,] -0.925047347 -1.2044307154 -1.0680019599 -0.893873062
## [155,] 1.826492899 0.3288645715 0.1010049859 1.866768227
## [156,] 3.390087901 1.4481779364 0.6589365139 0.466707308
## [157,] -0.894706997 0.9798119742 0.2143310710 0.073372667
## [158,] -0.026636433 -1.1372579352 0.9530327956 0.362441660
## [159,] -0.970386917 0.1817371177 -0.2500663755 -0.200936402
## [160,] -0.969406870 0.5169782861 -0.0530161888 -0.047979551
## [161,] 0.655880718 1.4592848861 -1.1984338560 1.494489006
## [162,] -1.052152140 -0.3942984941 -0.5835206404 -0.365691128
## [163,] -0.198422354 -2.4027880287 0.2199424464 -0.009131037
## [164,] -0.866074733 0.4276110049 -0.1121833304 -0.215613772
## [165,] 0.675019418 0.3745707730 -1.8374436293 0.972257923
## [166,] 0.628645183 -1.4678549959 -0.0810003790 0.957704120
## [167,] 0.915856252 1.2083027455 -1.3626640042 1.060713792
## [168,] -1.026299834 -0.0536874444 -0.3849069210 -0.240723350
## [169,] 0.142791800 -0.4864577553 1.3248292074 0.454224690
## [170,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [171,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [172,] 2.805324565 -0.1857046418 -0.2642717824 0.431480320
## [173,] -0.070486344 -0.9792102723 1.0487705693 0.488816383
## [174,] -0.663931846 1.0296359635 0.2288381769 -0.186321580
## [175,] 2.352736343 -0.2275794585 -0.2598911857 0.966460288
## [176,] -0.945222724 0.2988465531 -0.1828216316 -0.177900756
## [177,] -1.064906265 -0.5087286154 -0.6499852562 -0.402691984
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## [495,] 0.021367562 1.9897997448 -0.0481851196 0.965723695
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## [498,] -0.384373271 3.2118462101 1.4940062621 0.474799055
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## [503,] -0.964424525 0.4063774405 -0.1183658456 -0.104939485
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## [506,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [507,] 2.214952369 -0.7040329041 -0.5312040706 0.916097420
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## [509,] 1.445664747 -2.1683604967 -1.3428941655 1.184805303
## [510,] 1.534375252 1.7885461213 -1.0611309074 0.570099349
## [511,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [512,] 1.073734558 2.1358006292 -0.8274365011 1.293877196
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## [514,] 0.059201877 -1.4537551579 0.7614402290 0.111786995
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## [516,] 0.628989240 -1.3561041888 -0.0153158913 1.008670186
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## [518,] 0.826856211 -0.5316493414 0.4567625403 1.145480593
## [519,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [520,] 2.051681755 2.4586144052 -0.7002974230 0.244733868
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## [522,] 0.620806875 1.1446020526 -1.3812115495 1.392736652
## [523,] -0.649575756 1.3119267355 0.3938977856 -0.074093581
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## [528,] -0.892725581 1.0360780218 0.2472870575 0.096819572
## [529,] 0.398058344 -0.1521547982 1.5050330526 0.295353056
## [530,] -0.423827822 0.4672531492 -0.1172140079 -0.738956530
## [531,] -0.690140229 2.5874489786 1.1464706851 0.562116364
## [532,] -0.907820490 0.3627598990 -0.1476390034 -0.194313352
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## [535,] -0.104093527 -1.4890103767 0.7511750695 0.295545414
## [536,] 0.515229071 0.0406569652 1.6108929883 0.240529183
## [537,] 6.863676311 2.2690746189 -1.1200948062 -5.735151130
## [538,] 1.400456943 0.5870298479 -1.7590093736 0.181590361
## [539,] -1.024816185 -0.2767201788 -0.5161393741 -0.345099393
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## [541,] -0.400223903 2.0916588243 0.8363812565 -0.020896392
## [542,] 0.951488913 0.3784218357 -1.8528954919 0.635466626
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## [546,] 2.377351952 -1.1207850191 0.8086706795 -2.573886970
## [547,] -0.361777480 0.4806497197 -0.1133133674 -0.808782579
## [548,] 1.393895544 -1.9980630309 -1.2394463610 1.326510863
## [549,] 0.525150940 0.2863761430 -1.8796961683 1.115230232
## [550,] -0.554729254 2.0583013637 0.8266686618 0.152970469
## [551,] -0.767697146 1.5656158294 0.5506295269 0.187213031
## [552,] -0.886348518 1.0932930825 0.2805193655 0.115320000
## [553,] 1.964607033 1.9372707439 -1.0012540266 0.111630608
## [554,] -0.904066670 0.9777912355 0.2137426984 0.083905228
## [555,] 4.140273072 -0.6233887932 -0.6071621510 -1.404550452
## [556,] -0.717413457 0.6272215278 -0.0043438198 -0.305874364
## [557,] 1.496049864 -1.1942723936 -0.7733846673 1.571027950
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## [561,] 0.113486911 0.0655979953 1.6513013259 0.743968043
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## [563,] 1.680024423 -0.8804690868 0.9946549267 -1.609438999
## [564,] 1.969285136 -0.7570720703 -0.5466473302 1.192549919
## [565,] -0.315417761 1.4399091800 0.4477352267 -0.424449254
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## [567,] -0.773902181 1.5642761724 0.5502394628 0.194195636
## [568,] -1.050739105 -0.3381551591 -0.5506003837 -0.341604616
## [569,] 4.267814319 0.5209124195 0.0574840074 -1.034541892
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## [571,] -0.959908973 0.4631906041 -0.0852505569 -0.084344275
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## [580,] -0.083240468 -1.0936403936 0.9823059535 0.451815527
## [581,] 2.466630825 -0.3197741702 1.2739229903 -2.314880978
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## [586,] 0.391678276 0.2931738592 1.7672834236 0.507945575
## [587,] 6.857299249 2.2118595583 -1.1533271141 -5.753651558
## [588,] -0.058732173 0.8252680362 0.0698939709 -1.021420270
## [589,] 4.591895143 -0.3583695147 -0.4802777633 -1.835736725
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## [594,] 0.011625941 -0.7939675713 1.1524266431 0.473444228
## [595,] -0.486701495 -0.2163803329 -0.5151435620 -0.976323397
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## [608,] 0.493317750 0.0003120929 -2.0458544313 1.022669439
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## [656,] 1.150931821 0.6804485484 1.9463377286 -0.243745737
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## [661,] 0.741663353 -1.0069974816 -2.6540399679 0.255347188
## [662,] 1.476918676 -1.3659175755 -0.8730815910 1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,] 2.482590756 0.1913237442 -0.0219082027 1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,] 1.777909122 -0.4633602706 -0.3616891289 1.561967520
## [672,] 0.575960104 0.8278092592 -1.5646035940 1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677 0.9775233041 0.2136646856 0.085301749
## [675,] 0.597246238 0.8603240333 -1.5468497792 1.290866650
## [676,] -0.678750309 0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416 2.8090080902 1.2772740678 0.674173273
## [679,] 1.448480112 -1.7070869943 -1.0718578891 1.393469238
## [680,] 0.249972874 -1.5242445278 0.7077697138 -0.154243300
## [681,] 0.262235704 0.0418743610 1.6278206191 0.550902494
## [682,] -0.110195557 -1.4903277955 0.7507914806 0.302412107
## [683,] 1.991958015 0.4711569300 1.7693867405 -1.369899663
## [684,] -0.612122816 1.5433658179 0.5275778906 -0.013533383
## [685,] 1.593931448 -0.8381103369 -0.5702430064 1.614940254
## [686,] -0.830295788 0.9378799892 0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,] 0.286865320 0.2705449081 1.7606946177 0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,] 0.088150689 -0.1073868437 1.5512143381 0.695449364
## [691,] 1.546048265 -0.6809334511 -0.4747587744 1.745853671
## [692,] -0.442495047 0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274 0.0630088408 -0.3177824728 -0.215534269
## [695,] 0.610906330 0.2846665856 1.7482332202 0.235568806
## [696,] -0.994346913 0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766 1.2674836128 0.3809574109 0.157554335
## [698,] 1.678284518 -0.5965455906 -0.4336146414 1.622723132
## [699,] 1.387203810 -1.3852868731 -0.8787212930 1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,] 2.591000816 1.1639797750 0.5430410319 1.314577051
## [703,] 0.141071518 -1.0452117911 0.9964067687 0.199394362
## [704,] -0.958409837 0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972 0.8846308877 0.360120609
## [706,] -0.957976849 0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772 0.0035276162 -0.3516746131 -0.222222922
## [708,] 1.040582830 -0.0946382622 0.7000179410 1.084707607
## [709,] -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## [710,] 0.152449418 -1.3777848985 0.8001334335 0.032530955
## [711,] 0.814167311 0.4046125825 -1.8286964431 0.815673010
## [712,] -0.195145312 0.5470983840 -0.8825814068 0.567452960
attach(Temp2)
## The following objects are masked from train:
##
## Age, Embarked, Fare, Sex, Survived
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.2.2
##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
# Identifying the scores by their survival status
titanictyp_pca <- cbind(data.frame(Survived),Temp2_pca$x)
titanictyp_pca
## Survived PC1 PC2 PC3 PC4
## 1 0 -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## 2 1 2.328844131 0.1022918285 -0.0644045317 1.147406212
## 3 1 -0.076863406 -1.0364253330 1.0155382614 0.470315955
## 4 1 0.541154997 -0.4004517724 1.3498713191 0.005941459
## 5 0 -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## 6 0 -0.278861772 1.7828311382 0.6470218066 -0.311526470
## 7 0 -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
## 8 1 -0.030671121 -0.9706142289 1.0512734542 0.444011801
## 9 1 1.664344689 -1.3812908595 -0.8941309506 1.278937145
## 10 1 -0.108260428 -2.2716456857 0.2912731112 -0.059238176
## 11 1 0.358340114 0.8443588327 2.0935020004 0.802227620
## 12 0 -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
## 13 0 -0.630009991 0.8694448494 0.1324763008 -0.301524135
## 14 0 -0.154266787 -1.7231957561 0.6166953333 0.249299556
## 15 1 0.208282705 0.6444468869 1.9855747253 0.894059299
## 16 0 -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
## 17 0 0.080053345 -0.7233559402 1.1895595915 0.422118607
## 18 0 -0.720981351 0.6264512250 -0.0045681066 -0.301859366
## 19 1 -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## 20 1 0.625733012 -1.5243219921 -0.1140148752 0.935304605
## 21 1 -0.647725138 0.2513992845 -0.2297830451 -0.564031854
## 22 0 -0.028458129 -2.0310634439 0.4276154032 -0.046334256
## 23 1 0.290832573 -0.2869811981 1.4326297117 0.364662359
## 24 0 2.118171868 0.3460076983 -0.3513946758 -3.907620912
## 25 0 0.875161156 1.1995167387 -1.3652222002 1.106508508
## 26 0 -0.715648479 2.3585887361 1.0135414535 0.488114652
## 27 0 1.474364633 0.6588246642 -1.7215319207 0.124097704
## 28 0 -0.353680136 1.0966188162 0.2483413792 -0.535451822
## 29 0 -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
## 30 0 -0.002848466 -1.4671517284 0.7575395885 0.181613043
## 31 1 1.430674269 -1.4317399327 -0.9088200604 1.541889474
## 32 0 0.031651073 -0.2312615472 1.4819997708 0.707675872
## 33 0 0.091775301 -0.9441782404 1.0589707441 0.306221266
## 34 1 1.737017034 -1.9798219080 -1.2507083116 0.914715217
## 35 1 0.649379751 -1.2958636466 0.0187973373 1.011401099
## 36 0 -0.005330479 -1.4676875913 0.7573835629 0.184406085
## 37 0 -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
## 38 0 -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
## 39 1 2.466575808 0.7462487722 0.3053993550 1.274857785
## 40 1 0.166579768 -0.8163515486 1.1293360004 0.273396074
## 41 0 1.459736803 2.7216822690 -0.5076885621 1.090593468
## 42 1 -0.076792792 -1.3156014023 0.8513855516 0.341853400
## 43 0 0.547522780 0.4866401084 -1.7633798140 1.179923077
## 44 1 0.035247891 -2.1848242042 0.3331258345 -0.195053315
## 45 0 -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
## 46 0 0.506071875 0.1147422142 -1.9793898155 1.059670295
## 47 0 0.056057955 1.3525954097 0.3725928346 -0.919505513
## 48 0 -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
## 49 1 -0.025776293 -0.8578809172 1.1172440150 0.489856824
## 50 0 -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
## 51 1 -0.134256967 -1.5513608787 0.7164474901 0.303812103
## 52 0 -0.993534474 0.0650630709 -0.3171843486 -0.226241395
## 53 0 -0.932468599 0.4132766744 -0.1163570157 -0.140899900
## 54 0 0.343048387 -1.5041496720 0.7136206745 -0.258982373
## 55 0 -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## 56 0 0.621242869 0.3629605012 -1.8408241584 1.032773366
## 57 1 -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## 58 0 -1.012476731 0.0051352047 -0.3512065362 -0.230602048
## 59 1 -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
## 60 1 0.005110655 -0.7953742112 1.1520170759 0.480775963
## 61 0 -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
## 62 1 -0.964009855 0.2389521784 -0.2168340676 -0.182435974
## 63 0 -0.503768344 0.2824793282 -0.2207335593 -0.726028287
## 64 1 -0.102301041 -1.5444616449 0.7184563199 0.267851688
## 65 1 0.066125823 -0.6146863442 1.2543469319 0.489144664
## 66 0 -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
## 67 1 3.069503611 -0.5246444689 1.1148325103 -3.147361192
## 68 0 -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
## 69 0 -0.982004454 0.2350671729 -0.2179652533 -0.162186420
## 70 0 -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## 71 0 -0.214309508 1.3500617657 0.3884282861 -0.589580909
## 72 0 -0.845699534 0.0969804002 -0.3078910727 -0.392601955
## 73 0 -0.800620638 1.9493755407 0.7783798817 0.403998588
## 74 0 1.158894058 2.9917603749 -0.3296117147 1.583195391
## 75 1 1.209014909 0.3223447643 -1.9023696200 0.294316071
## 76 1 0.161234875 -0.5383141877 1.2931571557 0.407793843
## 77 0 -0.727358414 0.5692361643 -0.0378004145 -0.320359794
## 78 0 -0.064471655 -0.9220734477 1.0819800975 0.507724595
## 79 0 -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
## 80 0 -0.948998041 0.4655462570 -0.0845646682 -0.096622488
## 81 0 -0.932539213 0.6924527437 0.0477956940 -0.012437345
## 82 0 -0.990295149 0.1774389620 -0.2513178570 -0.178533413
## 83 1 -0.112161487 -1.3232374475 0.8491621866 0.381654248
## 84 0 -0.926524525 0.7495895684 0.0810052222 0.006470867
## 85 0 -0.321794824 1.3826941194 0.4145029188 -0.442949682
## 86 0 1.473730145 -1.3945251058 -0.8896977450 1.506276452
## 87 0 -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
## 88 0 -0.091546650 -1.3746250000 0.8176266572 0.332779489
## 89 0 1.489723682 -1.2514764691 -0.8066137767 1.552470265
## 90 0 -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## 91 0 0.050371589 2.7498782185 0.3968624480 1.279719438
## 92 0 -0.821294068 0.2697642906 -0.2078625945 -0.343035886
## 93 0 3.500861199 0.8729890093 -1.7254669726 -2.259051431
## 94 0 0.059862195 -2.3470248039 0.2361788623 -0.299781963
## 95 0 -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## 96 0 0.856496849 0.7767001720 -1.6126312086 0.934937055
## 97 1 0.027568597 -0.6509299197 1.2355074129 0.519695298
## 98 0 0.036664218 1.8509526994 0.6668565633 -0.666591926
## 99 1 0.492096651 -0.4466576443 -2.3085826307 0.818630611
## 100 1 -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## 101 0 -0.893312280 1.1476278804 0.3129130357 0.148833028
## 102 0 0.584492113 0.7458939120 -1.6133143950 1.253865794
## 103 0 -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## 104 0 0.138651104 0.1827074307 1.7185460698 0.767003689
## 105 1 0.166579768 -0.8163515486 1.1293360004 0.273396074
## 106 0 -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## 107 0 0.609453478 0.1929004015 -1.9400595584 0.969010264
## 108 1 0.106324917 -1.3877431053 0.7972339315 0.084435450
## 109 0 -0.371914372 0.8134907585 0.0830379805 -0.643315693
## 110 0 -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## 111 0 1.411988553 0.4220047153 -1.8567787569 0.091583837
## 112 1 -0.104543417 -1.2657544555 0.8824725073 0.398758155
## 113 1 0.008732262 -1.1296218900 0.9552561607 0.322640812
## 114 0 -0.290457192 -0.1993767184 -1.3153815378 0.340912606
## 115 0 -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## 116 0 -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## 117 1 -0.997913218 0.1199559700 -0.2846281777 -0.195637320
## 118 0 0.142972844 -1.9382135057 0.4712234148 -0.213571117
## 119 0 -0.711415758 0.7122738159 0.0452803553 -0.274108724
## 120 0 -0.837672804 0.9921255660 0.2179163837 0.009191356
## 121 0 -0.786174026 1.5057884376 0.5166365941 0.182328683
## 122 1 0.625789110 -1.1080768203 0.9283830454 -0.423094436
## 123 0 -0.813012301 1.7512662798 0.6626909065 0.328074922
## 124 0 -0.828623295 0.9103219462 0.1692381139 -0.039507101
## 125 0 1.363011889 1.9190638316 -0.9734089498 0.839966602
## 126 1 0.628437935 -1.4678997405 -0.0810134072 0.957937339
## 127 0 -0.975627392 0.2922822335 -0.1847329454 -0.143685992
## 128 0 -0.786447467 1.1148615610 0.2867993966 0.002900062
## 129 1 0.109524253 -0.2144488512 1.4868950745 0.620044181
## 130 0 -1.004548410 0.0626851796 -0.3178767123 -0.213847271
## 131 0 -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## 132 0 -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## 133 1 -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## 134 0 0.292191896 0.1041801184 1.6625351704 0.542869023
## 135 0 -0.387165823 0.3076536277 -0.2134036318 -0.857242604
## 136 0 -0.462102217 2.1341376573 0.8653228600 0.074412689
## 137 0 -0.108437846 -0.9976529748 -1.7964107906 -0.249065381
## 138 1 -0.196474743 -2.4582058055 0.1872334484 -0.036999327
## 139 0 -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## 140 0 1.014114107 2.1229286683 -0.8311843925 1.360968857
## 141 0 -1.054582031 -0.3948231038 -0.5836733895 -0.362956740
## 142 0 1.877062338 0.6748120111 0.3011724864 1.963921497
## 143 0 -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## 144 0 -1.037266068 0.6140041188 0.0083808710 0.079736514
## 145 0 -0.819925729 -0.8467055469 -0.8644051723 -0.858108061
## 146 1 -0.776470582 -1.2840297533 -1.1243249106 -1.112421644
## 147 1 -0.042176813 -2.2573783381 0.2954272933 -0.133602918
## 148 1 -0.650385190 1.2000754541 0.3281840430 -0.124535951
## 149 0 -0.047950783 1.0255835534 -0.6106769508 0.607226009
## 150 0 -0.939278650 0.6351594471 0.0145406064 -0.030529989
## 151 1 0.024380066 -0.6795374501 1.2188912589 0.510445084
## 152 0 -0.984345239 -0.3238208286 -0.5464266984 -0.416318488
## 153 1 -0.122381475 -1.4371204529 0.7828568729 0.341801696
## 154 1 -0.925047347 -1.2044307154 -1.0680019599 -0.893873062
## 155 1 1.826492899 0.3288645715 0.1010049859 1.866768227
## 156 1 3.390087901 1.4481779364 0.6589365139 0.466707308
## 157 0 -0.894706997 0.9798119742 0.2143310710 0.073372667
## 158 0 -0.026636433 -1.1372579352 0.9530327956 0.362441660
## 159 0 -0.970386917 0.1817371177 -0.2500663755 -0.200936402
## 160 0 -0.969406870 0.5169782861 -0.0530161888 -0.047979551
## 161 0 0.655880718 1.4592848861 -1.1984338560 1.494489006
## 162 1 -1.052152140 -0.3942984941 -0.5835206404 -0.365691128
## 163 0 -0.198422354 -2.4027880287 0.2199424464 -0.009131037
## 164 0 -0.866074733 0.4276110049 -0.1121833304 -0.215613772
## 165 1 0.675019418 0.3745707730 -1.8374436293 0.972257923
## 166 1 0.628645183 -1.4678549959 -0.0810003790 0.957704120
## 167 1 0.915856252 1.2083027455 -1.3626640042 1.060713792
## 168 0 -1.026299834 -0.0536874444 -0.3849069210 -0.240723350
## 169 1 0.142791800 -0.4864577553 1.3248292074 0.454224690
## 170 0 -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## 171 0 -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## 172 1 2.805324565 -0.1857046418 -0.2642717824 0.431480320
## 173 1 -0.070486344 -0.9792102723 1.0487705693 0.488816383
## 174 0 -0.663931846 1.0296359635 0.2288381769 -0.186321580
## 175 1 2.352736343 -0.2275794585 -0.2598911857 0.966460288
## 176 0 -0.945222724 0.2988465531 -0.1828216316 -0.177900756
## 177 1 -1.064906265 -0.5087286154 -0.6499852562 -0.402691984
## 178 0 -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## 179 0 -0.841709082 1.4937985069 0.5131455209 0.244822996
## 180 1 0.092394215 0.9695725098 0.1450570150 -1.140131503
## 181 0 -1.010510802 -0.1619551432 -0.4495772422 -0.309844189
## 182 1 -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## 183 0 -1.046137539 -0.2534042938 -0.5010639731 -0.308267890
## 184 0 -0.990722301 -0.3810358893 -0.5796590064 -0.434818916
## 185 1 0.918110825 -0.3190676064 1.3735677099 -0.418251785
## 186 0 -0.985417223 0.2343303615 -0.2181797885 -0.158345987
## 187 0 -0.723057710 1.9661212539 0.7832556823 0.316716027
## 188 1 0.080389515 -2.1750781991 0.3359635504 -0.245851765
## 189 0 -0.983485098 -0.0444438107 -0.3822154791 -0.288903324
## 190 0 -0.663587790 1.1413867707 0.2945226647 -0.135355514
## 191 1 0.035763975 -2.0171979934 0.4316525661 -0.118604217
## 192 0 -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## 193 0 -0.904063665 0.4752475176 -0.0817399805 -0.147187719
## 194 0 -0.951599786 0.2416314925 -0.2160539395 -0.196401184
## 195 0 -1.038123204 -0.1679166171 -0.4513130272 -0.278771597
## 196 0 0.557036252 0.5724514462 -1.7135346287 1.207732372
## 197 0 0.902107564 1.4540526970 -0.4196281764 -0.359180401
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## 709 0 -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## 710 1 0.152449418 -1.3777848985 0.8001334335 0.032530955
## 711 1 0.814167311 0.4046125825 -1.8286964431 0.815673010
## 712 0 -0.195145312 0.5470983840 -0.8825814068 0.567452960
# Means of scores for all the PC's classified by Survival status
length(titanictyp_pca[, 2:5])
## [1] 4
length(Temp2$Survived)
## [1] 712
Temp2$Survived <- factor(Temp2$Survived, levels = c(0, 1))
tabmeansPC <- aggregate(titanictyp_pca[,2:5],by=list(Survived=Temp2$Survived),mean)
tabmeansPC
## Survived PC1 PC2 PC3 PC4
## 1 0 -0.4248113 0.2427335 -0.1708880 -0.04404456
## 2 1 0.6254167 -0.3573577 0.2515851 0.06484338
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$Survived)),]
tabmeansPC
## Survived PC1 PC2 PC3 PC4
## 2 1 0.6254167 -0.3573577 0.2515851 0.06484338
## 1 0 -0.4248113 0.2427335 -0.1708880 -0.04404456
tabfmeans <- t(tabmeansPC[,-1])
tabfmeans
## 2 1
## PC1 0.62541668 -0.42481133
## PC2 -0.35735772 0.24273355
## PC3 0.25158512 -0.17088801
## PC4 0.06484338 -0.04404456
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$Survived))
tabfmeans
## 1 0
## PC1 0.62541668 -0.42481133
## PC2 -0.35735772 0.24273355
## PC3 0.25158512 -0.17088801
## PC4 0.06484338 -0.04404456
# Standard deviations of scores for all the PC's classified by Survival status
tabsdsPC <- aggregate(titanictyp_pca[,2:5],by=list(Survived=Temp2$Survived),sd)
tabfsds <- t(tabsdsPC[,-1])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$Survived))
tabfsds
## 0 1
## PC1 0.7837685 1.376398
## PC2 0.9805745 1.025566
## PC3 0.7769647 1.036368
## PC4 0.6478594 1.034475
t.test(PC1~Temp2$Survived,data=titanictyp_pca)
##
## Welch Two Sample t-test
##
## data: PC1 by Temp2$Survived
## t = -11.722, df = 413.73, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -1.2263414 -0.8741146
## sample estimates:
## mean in group 0 mean in group 1
## -0.4248113 0.6254167
t.test(PC2~Temp2$Survived,data=titanictyp_pca)
##
## Welch Two Sample t-test
##
## data: PC2 by Temp2$Survived
## t = 7.7995, df = 597.72, p-value = 2.782e-14
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## 0.4489854 0.7511971
## sample estimates:
## mean in group 0 mean in group 1
## 0.2427335 -0.3573577
t.test(PC3~Temp2$Survived,data=titanictyp_pca)
##
## Welch Two Sample t-test
##
## data: PC3 by Temp2$Survived
## t = -5.8852, df = 498.65, p-value = 7.302e-09
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.5635121 -0.2814342
## sample estimates:
## mean in group 0 mean in group 1
## -0.1708880 0.2515851
t.test(PC4~Temp2$Survived,data=titanictyp_pca)
##
## Welch Two Sample t-test
##
## data: PC4 by Temp2$Survived
## t = -1.5873, df = 439.14, p-value = 0.1132
## alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
## 95 percent confidence interval:
## -0.24370885 0.02593297
## sample estimates:
## mean in group 0 mean in group 1
## -0.04404456 0.06484338
## F ratio tests
var.test(PC1~Temp2$Survived,data=titanictyp_pca)
##
## F test to compare two variances
##
## data: PC1 by Temp2$Survived
## F = 0.32426, num df = 423, denom df = 287, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.2616503 0.4000869
## sample estimates:
## ratio of variances
## 0.3242558
var.test(PC2~Temp2$Survived,data=titanictyp_pca)
##
## F test to compare two variances
##
## data: PC2 by Temp2$Survived
## F = 0.91419, num df = 423, denom df = 287, p-value = 0.4019
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.7376795 1.1279785
## sample estimates:
## ratio of variances
## 0.9141855
var.test(PC3~Temp2$Survived,data=titanictyp_pca)
##
## F test to compare two variances
##
## data: PC3 by Temp2$Survived
## F = 0.56205, num df = 423, denom df = 287, p-value = 6.934e-08
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.4535319 0.6934912
## sample estimates:
## ratio of variances
## 0.5620493
var.test(PC4~Temp2$Survived,data=titanictyp_pca)
##
## F test to compare two variances
##
## data: PC4 by Temp2$Survived
## F = 0.39221, num df = 423, denom df = 287, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.3164865 0.4839364
## sample estimates:
## ratio of variances
## 0.3922128
# Levene's tests (one-sided)
library(car)
## Warning: package 'car' was built under R version 4.2.2
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.2.2
##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
##
## recode
(LTPC1 <- leveneTest(PC1~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 42.423 1.392e-10 ***
## 710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 6.959925e-11
(LTPC2 <- leveneTest(PC2~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 3.0413 0.0816 .
## 710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.04080225
(LTPC3 <- leveneTest(PC3~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 46.202 2.262e-11 ***
## 710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC3_1sided <- LTPC3[[3]][1]/2)
## [1] 1.131124e-11
(LTPC4 <- leveneTest(PC4~Temp2$Survived,data=titanictyp_pca))
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 31.576 2.756e-08 ***
## 710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(p_PC4_1sided <- LTPC4[[3]][1]/2)
## [1] 1.378021e-08
# Plotting the scores for the first and second components
plot(titanictyp_pca$PC1, titanictyp_pca$PC2,pch=ifelse(titanictyp_pca$Survived == "S",1,16),xlab="PC1", ylab="PC2", main="49 Temp2 against values for PC1 & PC2")
abline(h=0)
abline(v=0)
legend("bottomleft", legend=c("Survivor","Nonsurvivor"), pch=c(1,16))
plot(eigen_Temp2, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")
plot(log(eigen_Temp2), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")
print(summary(Temp2_pca))
## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.1816 1.0409 0.9142 0.8274
## Proportion of Variance 0.3491 0.2709 0.2089 0.1711
## Cumulative Proportion 0.3491 0.6199 0.8289 1.0000
diag(cov(Temp2_pca$x))
## PC1 PC2 PC3 PC4
## 1.3962390 1.0834721 0.8357525 0.6845364
xlim <- range(Temp2_pca$x[,1])
Temp2_pca$x[,1]
## [1] -1.036571945 2.328844131 -0.076863406 0.541154997 -0.943742080
## [6] -0.278861772 -0.992543997 -0.030671121 1.664344689 -0.108260428
## [11] 0.358340114 -1.039398015 -0.630009991 -0.154266787 0.208282705
## [16] -0.121191971 0.080053345 -0.720981351 -0.888689303 0.625733012
## [21] -0.647725138 -0.028458129 0.290832573 2.118171868 0.875161156
## [26] -0.715648479 1.474364633 -0.353680136 -1.033020953 -0.002848466
## [31] 1.430674269 0.031651073 0.091775301 1.737017034 0.649379751
## [36] -0.005330479 -0.729676286 -1.036123470 2.466575808 0.166579768
## [41] 1.459736803 -0.076792792 0.547522780 0.035247891 -0.614660418
## [46] 0.506071875 0.056057955 -0.895091155 -0.025776293 -1.044431067
## [51] -0.134256967 -0.993534474 -0.932468599 0.343048387 -0.220781974
## [56] 0.621242869 -0.361657574 -1.012476731 -0.901655367 0.005110655
## [61] -1.014854325 -0.964009855 -0.503768344 -0.102301041 0.066125823
## [66] -0.738211213 3.069503611 -1.013889766 -0.982004454 -1.041827907
## [71] -0.214309508 -0.845699534 -0.800620638 1.158894058 1.209014909
## [76] 0.161234875 -0.727358414 -0.064471655 -0.173778840 -0.948998041
## [81] -0.932539213 -0.990295149 -0.112161487 -0.926524525 -0.321794824
## [86] 1.473730145 -1.026643890 -0.091546650 1.489723682 -1.034572211
## [91] 0.050371589 -0.821294068 3.500861199 0.059862195 -0.220781974
## [96] 0.856496849 0.027568597 0.036664218 0.492096651 -1.025161831
## [101] -0.893312280 0.584492113 -1.051808084 0.138651104 0.166579768
## [106] -0.946082865 0.609453478 0.106324917 -0.371914372 -1.050427438
## [111] 1.411988553 -0.104543417 0.008732262 -0.290457192 -1.009337404
## [116] -0.689606114 -0.997913218 0.142972844 -0.711415758 -0.837672804
## [121] -0.786174026 0.625789110 -0.813012301 -0.828623295 1.363011889
## [126] 0.628437935 -0.975627392 -0.786447467 0.109524253 -1.004548410
## [131] -1.050928035 -0.767938660 -0.954730098 0.292191896 -0.387165823
## [136] -0.462102217 -0.108437846 -0.196474743 -1.034572211 1.014114107
## [141] -1.054582031 1.877062338 -0.914197553 -1.037266068 -0.819925729
## [146] -0.776470582 -0.042176813 -0.650385190 -0.047950783 -0.939278650
## [151] 0.024380066 -0.984345239 -0.122381475 -0.925047347 1.826492899
## [156] 3.390087901 -0.894706997 -0.026636433 -0.970386917 -0.969406870
## [161] 0.655880718 -1.052152140 -0.198422354 -0.866074733 0.675019418
## [166] 0.628645183 0.915856252 -1.026299834 0.142791800 -1.036571945
## [171] -0.914197553 2.805324565 -0.070486344 -0.663931846 2.352736343
## [176] -0.945222724 -1.064906265 -0.933328740 -0.841709082 0.092394215
## [181] -1.010510802 -1.015370410 -1.046137539 -0.990722301 0.918110825
## [186] -0.985417223 -0.723057710 0.080389515 -0.983485098 -0.663587790
## [191] 0.035763975 -1.015370410 -0.904063665 -0.951599786 -1.038123204
## [196] 0.557036252 0.902107564 -0.085101979 -0.008021331 -0.378687788
## [201] -0.599817166 -0.026241670 -0.541975130 -0.875726341 0.171281245
## [206] 1.576021360 0.923765970 7.783122743 0.300498078 -0.858188104
## [211] 0.053228880 -1.011757819 -0.906960350 -0.672282725 -1.010925472
## [216] 1.933332924 1.565398897 -1.107413754 0.162439072 0.880591976
## [221] 1.028205947 0.042129017 -0.089306659 0.133484249 0.015297746
## [226] -0.990811408 -1.046911665 -1.045775078 0.594006912 -0.957632792
## [231] -1.028557523 -0.837672804 0.666907557 0.803320697 2.453348419
## [236] 0.665415513 -0.078138217 -1.015803398 0.515637469 1.552483175
## [241] 4.592488314 -1.145676128 0.619772454 2.661751642 0.765215150
## [246] 2.099692269 2.386934820 4.572763956 0.147448581 -0.990295149
## [251] -0.666862335 -0.077742039 0.134694456 -0.748737987 1.902679142
## [256] 3.126121828 -1.036571945 -0.996672211 0.775010371 0.159170537
## [261] 3.114677909 -0.800431707 0.049888315 0.111388768 2.023443967
## [266] -0.622997025 0.879968183 -0.941426084 -0.255394947 3.132498891
## [271] -0.879971456 -0.539315078 -0.931424410 3.075880674 -0.926951678
## [276] -0.946082865 -0.875935179 -0.026636433 0.075396564 -1.050389038
## [281] -0.891501476 -1.005684998 0.461432438 -0.886514536 -0.970386917
## [286] 0.481832316 0.062642440 -0.665516910 0.805013470 1.668230548
## [291] -0.956152148 -0.985555446 2.518366521 2.214952369 1.123523486
## [296] -1.071439868 -1.045775078 2.099575543 -0.060343441 -0.110748452
## [301] 3.072971793 0.453398283 -1.049187846 4.293322569 1.403617766
## [306] -0.964424525 0.527503921 -0.239913161 -0.678431042 0.049888315
## [311] 1.459216011 0.451942143 -1.036175592 -0.989932775 2.754308066
## [316] 0.019280820 -1.029798530 -0.045856727 -0.650833665 -0.989862160
## [321] -0.005471708 -0.919785089 -1.001135641 -0.085169588 -0.891582983
## [326] -0.105973355 -0.789408756 -0.845432102 -1.015020343 -1.036433722
## [331] 1.757783372 -0.887899777 0.279130525 -0.064898808 -0.914197553
## [336] 0.022456956 -0.265500247 -0.984176216 0.016245912 -0.901214683
## [341] 0.160202706 0.102809144 -0.962873267 -0.758795250 0.249481579
## [346] -1.070008516 -0.254264370 1.237470265 0.219497592 0.044721460
## [351] 2.405139675 -0.938845662 0.271715283 -1.021403416 -1.010925472
## [356] -0.001128184 -0.225464960 -0.016118675 -0.720532876 1.472767262
## [361] -0.556725983 -0.692886669 0.811752906 1.694326912 0.558983863
## [366] -0.522843943 0.108142017 -0.631254003 -0.950119142 -0.489330748
## [371] -0.799410430 -0.937020961 -0.580237504 1.445664747 -0.917009726
## [376] 0.213805637 1.519713505 -0.078637400 -0.789408756 -0.994466645
## [381] -1.033211299 -0.175773979 -0.627414543 -0.848086144 0.179719640
## [386] 1.565787300 0.999086522 1.014510286 -0.975627392 -1.012126664
## [391] -1.042949008 -0.537594796 1.343183574 -1.033020953 2.517541600
## [396] 1.699155610 -1.017044405 -1.050928035 0.660530495 0.013916019
## [401] 0.834487097 1.742305211 0.192088017 -0.808745776 -0.399919948
## [406] -0.214276500 -0.711036394 2.283404562 -1.020767426 -0.544917926
## [411] 0.006109019 0.211219205 -0.964786899 1.010636449 -1.028557523
## [416] 2.202001714 -0.140940282 0.108142017 -0.919785089 -0.977452092
## [421] -0.005600916 0.474186563 -0.042202731 0.029386913 -0.650385190
## [426] 2.713938533 1.956478889 0.769672284 0.104501632 0.117255756
## [431] -0.740112539 1.915656287 -0.536046543 0.102809144 -0.801680601
## [436] -0.759753800 1.760541037 -0.771997850 0.506019753 -0.104233166
## [441] -0.541975130 1.999422833 0.896150563 0.104492616 -0.913770400
## [446] -0.920746643 -0.814087664 -1.047688710 0.105460181 -0.965303158
## [451] -0.741156728 0.635827880 -0.709795388 -1.064906265 -0.965730136
## [456] 0.037134190 0.601411438 -0.964424525 0.190711792 2.826659903
## [461] -0.599817166 1.003589877 0.762232253 -0.780967356 1.641562798
## [466] -1.026643890 -0.955221393 2.504787476 -0.877145386 -0.708227227
## [471] -0.737562916 -0.954364257 1.295032960 0.147104525 -0.886348518
## [476] 0.828746136 -0.844289504 -0.977541024 -0.716152542 1.858181219
## [481] 1.818545801 0.295813503 -0.943742080 0.618687125 -0.871315208
## [486] 0.024588903 0.168484098 -0.970730973 0.627619931 -0.346802476
## [491] 0.598958458 -1.035450844 -0.933119902 -0.476736169 0.021367562
## [496] 0.760369327 -1.003049274 -0.384373271 -0.854067028 0.858634719
## [501] 0.062617651 -0.001128184 -0.964424525 -0.743387084 0.412967328
## [506] -1.041827907 2.214952369 0.017978214 1.445664747 1.534375252
## [511] -1.047688710 1.073734558 -0.100648369 0.059201877 -1.028264174
## [516] 0.628989240 -0.201650787 0.826856211 -0.958836989 2.051681755
## [521] 0.710618450 0.620806875 -0.649575756 -0.944242677 -1.040949274
## [526] -0.150634288 -0.946082865 -0.892725581 0.398058344 -0.423827822
## [531] -0.690140229 -0.907820490 -1.055564909 -1.010701235 -0.104093527
## [536] 0.515229071 6.863676311 1.400456943 -1.024816185 -0.595529231
## [541] -0.400223903 0.951488913 -0.685036850 -1.019455804 -1.055306779
## [546] 2.377351952 -0.361777480 1.393895544 0.525150940 -0.554729254
## [551] -0.767697146 -0.886348518 1.964607033 -0.904066670 4.140273072
## [556] -0.717413457 1.496049864 -0.239887753 -1.003565532 -0.695473102
## [561] 0.113486911 -0.672774020 1.680024423 1.969285136 -0.315417761
## [566] -0.964217103 -0.773902181 -1.050739105 4.267814319 -0.038530417
## [571] -0.959908973 0.106777812 -1.070887148 -0.888689303 -0.786656305
## [576] -0.435684996 -1.031796848 0.110906488 -0.784751975 -0.083240468
## [581] 2.466630825 0.579363483 -0.958836989 -0.958836989 -0.885291934
## [586] 0.391678276 6.857299249 -0.058732173 4.591895143 -0.913988715
## [591] -0.970801588 0.060668911 -0.913503430 0.011625941 -0.486701495
## [596] -0.201522375 -0.030076997 -1.073762336 -0.938501605 -1.022180461
## [601] 0.771736622 -1.082621690 -0.991536156 -1.009337404 -0.950119142
## [606] 0.942897157 -0.916959019 0.493317750 1.377765637 -1.068319034
## [611] 0.951681199 0.721112588 -0.958995120 -0.995895167 -0.863270160
## [616] 0.152781454 0.288776122 -1.055875161 -0.154315904 2.555909698
## [621] 1.374501807 0.474767141 -0.709603452 -1.019922772 -1.017440758
## [626] -0.133206306 -0.082929597 -1.005126093 1.552283925 -0.842145536
## [631] -1.009426336 -0.856803991 0.293242383 -0.035567539 0.557088374
## [636] 0.149998204 -0.888689303 0.182436410 0.292515584 0.384432832
## [641] -1.008099402 -0.972663098 -1.018134881 -0.129741415 -0.856803991
## [646] 0.528400872 -1.003152277 -0.718431729 -0.913337412 0.085370444
## [651] -0.972438860 -0.095994593 0.932975224 -0.912581690 -0.856828781
## [656] 1.150931821 -0.987157412 -1.024511943 -0.014020532 -0.761561598
## [661] 0.741663353 1.476918676 -1.028858569 -1.022696720 -1.049049623
## [666] 2.482590756 -1.025419786 -0.361657574 -1.040949274 -1.034501597
## [671] 1.777909122 0.575960104 -1.050928035 -0.905307677 0.597246238
## [676] -0.678750309 -0.853207174 -0.698449416 1.448480112 0.249972874
## [681] 0.262235704 -0.110195557 1.991958015 -0.612122816 1.593931448
## [686] -0.830295788 -0.990206217 0.286865320 -0.952459927 0.088150689
## [691] 1.546048265 -0.442495047 -1.103167049 -1.003049274 0.610906330
## [696] -0.994346913 -0.855427766 1.678284518 1.387203810 -1.017112014
## [701] -1.047688710 2.591000816 0.141071518 -0.958409837 -0.070208481
## [706] -0.957976849 -1.019922772 1.040582830 -0.933328740 0.152449418
## [711] 0.814167311 -0.195145312
Temp2_pca$x
## PC1 PC2 PC3 PC4
## [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [2,] 2.328844131 0.1022918285 -0.0644045317 1.147406212
## [3,] -0.076863406 -1.0364253330 1.0155382614 0.470315955
## [4,] 0.541154997 -0.4004517724 1.3498713191 0.005941459
## [5,] -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## [6,] -0.278861772 1.7828311382 0.6470218066 -0.311526470
## [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
## [8,] -0.030671121 -0.9706142289 1.0512734542 0.444011801
## [9,] 1.664344689 -1.3812908595 -0.8941309506 1.278937145
## [10,] -0.108260428 -2.2716456857 0.2912731112 -0.059238176
## [11,] 0.358340114 0.8443588327 2.0935020004 0.802227620
## [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
## [13,] -0.630009991 0.8694448494 0.1324763008 -0.301524135
## [14,] -0.154266787 -1.7231957561 0.6166953333 0.249299556
## [15,] 0.208282705 0.6444468869 1.9855747253 0.894059299
## [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
## [17,] 0.080053345 -0.7233559402 1.1895595915 0.422118607
## [18,] -0.720981351 0.6264512250 -0.0045681066 -0.301859366
## [19,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [20,] 0.625733012 -1.5243219921 -0.1140148752 0.935304605
## [21,] -0.647725138 0.2513992845 -0.2297830451 -0.564031854
## [22,] -0.028458129 -2.0310634439 0.4276154032 -0.046334256
## [23,] 0.290832573 -0.2869811981 1.4326297117 0.364662359
## [24,] 2.118171868 0.3460076983 -0.3513946758 -3.907620912
## [25,] 0.875161156 1.1995167387 -1.3652222002 1.106508508
## [26,] -0.715648479 2.3585887361 1.0135414535 0.488114652
## [27,] 1.474364633 0.6588246642 -1.7215319207 0.124097704
## [28,] -0.353680136 1.0966188162 0.2483413792 -0.535451822
## [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
## [30,] -0.002848466 -1.4671517284 0.7575395885 0.181613043
## [31,] 1.430674269 -1.4317399327 -0.9088200604 1.541889474
## [32,] 0.031651073 -0.2312615472 1.4819997708 0.707675872
## [33,] 0.091775301 -0.9441782404 1.0589707441 0.306221266
## [34,] 1.737017034 -1.9798219080 -1.2507083116 0.914715217
## [35,] 0.649379751 -1.2958636466 0.0187973373 1.011401099
## [36,] -0.005330479 -1.4676875913 0.7573835629 0.184406085
## [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
## [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
## [39,] 2.466575808 0.7462487722 0.3053993550 1.274857785
## [40,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [41,] 1.459736803 2.7216822690 -0.5076885621 1.090593468
## [42,] -0.076792792 -1.3156014023 0.8513855516 0.341853400
## [43,] 0.547522780 0.4866401084 -1.7633798140 1.179923077
## [44,] 0.035247891 -2.1848242042 0.3331258345 -0.195053315
## [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
## [46,] 0.506071875 0.1147422142 -1.9793898155 1.059670295
## [47,] 0.056057955 1.3525954097 0.3725928346 -0.919505513
## [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
## [49,] -0.025776293 -0.8578809172 1.1172440150 0.489856824
## [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
## [51,] -0.134256967 -1.5513608787 0.7164474901 0.303812103
## [52,] -0.993534474 0.0650630709 -0.3171843486 -0.226241395
## [53,] -0.932468599 0.4132766744 -0.1163570157 -0.140899900
## [54,] 0.343048387 -1.5041496720 0.7136206745 -0.258982373
## [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [56,] 0.621242869 0.3629605012 -1.8408241584 1.032773366
## [57,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [58,] -1.012476731 0.0051352047 -0.3512065362 -0.230602048
## [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
## [60,] 0.005110655 -0.7953742112 1.1520170759 0.480775963
## [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
## [62,] -0.964009855 0.2389521784 -0.2168340676 -0.182435974
## [63,] -0.503768344 0.2824793282 -0.2207335593 -0.726028287
## [64,] -0.102301041 -1.5444616449 0.7184563199 0.267851688
## [65,] 0.066125823 -0.6146863442 1.2543469319 0.489144664
## [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
## [67,] 3.069503611 -0.5246444689 1.1148325103 -3.147361192
## [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
## [69,] -0.982004454 0.2350671729 -0.2179652533 -0.162186420
## [70,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [71,] -0.214309508 1.3500617657 0.3884282861 -0.589580909
## [72,] -0.845699534 0.0969804002 -0.3078910727 -0.392601955
## [73,] -0.800620638 1.9493755407 0.7783798817 0.403998588
## [74,] 1.158894058 2.9917603749 -0.3296117147 1.583195391
## [75,] 1.209014909 0.3223447643 -1.9023696200 0.294316071
## [76,] 0.161234875 -0.5383141877 1.2931571557 0.407793843
## [77,] -0.727358414 0.5692361643 -0.0378004145 -0.320359794
## [78,] -0.064471655 -0.9220734477 1.0819800975 0.507724595
## [79,] -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
## [80,] -0.948998041 0.4655462570 -0.0845646682 -0.096622488
## [81,] -0.932539213 0.6924527437 0.0477956940 -0.012437345
## [82,] -0.990295149 0.1774389620 -0.2513178570 -0.178533413
## [83,] -0.112161487 -1.3232374475 0.8491621866 0.381654248
## [84,] -0.926524525 0.7495895684 0.0810052222 0.006470867
## [85,] -0.321794824 1.3826941194 0.4145029188 -0.442949682
## [86,] 1.473730145 -1.3945251058 -0.8896977450 1.506276452
## [87,] -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
## [88,] -0.091546650 -1.3746250000 0.8176266572 0.332779489
## [89,] 1.489723682 -1.2514764691 -0.8066137767 1.552470265
## [90,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [91,] 0.050371589 2.7498782185 0.3968624480 1.279719438
## [92,] -0.821294068 0.2697642906 -0.2078625945 -0.343035886
## [93,] 3.500861199 0.8729890093 -1.7254669726 -2.259051431
## [94,] 0.059862195 -2.3470248039 0.2361788623 -0.299781963
## [95,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [96,] 0.856496849 0.7767001720 -1.6126312086 0.934937055
## [97,] 0.027568597 -0.6509299197 1.2355074129 0.519695298
## [98,] 0.036664218 1.8509526994 0.6668565633 -0.666591926
## [99,] 0.492096651 -0.4466576443 -2.3085826307 0.818630611
## [100,] -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## [101,] -0.893312280 1.1476278804 0.3129130357 0.148833028
## [102,] 0.584492113 0.7458939120 -1.6133143950 1.253865794
## [103,] -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## [104,] 0.138651104 0.1827074307 1.7185460698 0.767003689
## [105,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [106,] -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## [107,] 0.609453478 0.1929004015 -1.9400595584 0.969010264
## [108,] 0.106324917 -1.3877431053 0.7972339315 0.084435450
## [109,] -0.371914372 0.8134907585 0.0830379805 -0.643315693
## [110,] -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## [111,] 1.411988553 0.4220047153 -1.8567787569 0.091583837
## [112,] -0.104543417 -1.2657544555 0.8824725073 0.398758155
## [113,] 0.008732262 -1.1296218900 0.9552561607 0.322640812
## [114,] -0.290457192 -0.1993767184 -1.3153815378 0.340912606
## [115,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [116,] -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## [117,] -0.997913218 0.1199559700 -0.2846281777 -0.195637320
## [118,] 0.142972844 -1.9382135057 0.4712234148 -0.213571117
## [119,] -0.711415758 0.7122738159 0.0452803553 -0.274108724
## [120,] -0.837672804 0.9921255660 0.2179163837 0.009191356
## [121,] -0.786174026 1.5057884376 0.5166365941 0.182328683
## [122,] 0.625789110 -1.1080768203 0.9283830454 -0.423094436
## [123,] -0.813012301 1.7512662798 0.6626909065 0.328074922
## [124,] -0.828623295 0.9103219462 0.1692381139 -0.039507101
## [125,] 1.363011889 1.9190638316 -0.9734089498 0.839966602
## [126,] 0.628437935 -1.4678997405 -0.0810134072 0.957937339
## [127,] -0.975627392 0.2922822335 -0.1847329454 -0.143685992
## [128,] -0.786447467 1.1148615610 0.2867993966 0.002900062
## [129,] 0.109524253 -0.2144488512 1.4868950745 0.620044181
## [130,] -1.004548410 0.0626851796 -0.3178767123 -0.213847271
## [131,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [132,] -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## [133,] -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## [134,] 0.292191896 0.1041801184 1.6625351704 0.542869023
## [135,] -0.387165823 0.3076536277 -0.2134036318 -0.857242604
## [136,] -0.462102217 2.1341376573 0.8653228600 0.074412689
## [137,] -0.108437846 -0.9976529748 -1.7964107906 -0.249065381
## [138,] -0.196474743 -2.4582058055 0.1872334484 -0.036999327
## [139,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [140,] 1.014114107 2.1229286683 -0.8311843925 1.360968857
## [141,] -1.054582031 -0.3948231038 -0.5836733895 -0.362956740
## [142,] 1.877062338 0.6748120111 0.3011724864 1.963921497
## [143,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [144,] -1.037266068 0.6140041188 0.0083808710 0.079736514
## [145,] -0.819925729 -0.8467055469 -0.8644051723 -0.858108061
## [146,] -0.776470582 -1.2840297533 -1.1243249106 -1.112421644
## [147,] -0.042176813 -2.2573783381 0.2954272933 -0.133602918
## [148,] -0.650385190 1.2000754541 0.3281840430 -0.124535951
## [149,] -0.047950783 1.0255835534 -0.6106769508 0.607226009
## [150,] -0.939278650 0.6351594471 0.0145406064 -0.030529989
## [151,] 0.024380066 -0.6795374501 1.2188912589 0.510445084
## [152,] -0.984345239 -0.3238208286 -0.5464266984 -0.416318488
## [153,] -0.122381475 -1.4371204529 0.7828568729 0.341801696
## [154,] -0.925047347 -1.2044307154 -1.0680019599 -0.893873062
## [155,] 1.826492899 0.3288645715 0.1010049859 1.866768227
## [156,] 3.390087901 1.4481779364 0.6589365139 0.466707308
## [157,] -0.894706997 0.9798119742 0.2143310710 0.073372667
## [158,] -0.026636433 -1.1372579352 0.9530327956 0.362441660
## [159,] -0.970386917 0.1817371177 -0.2500663755 -0.200936402
## [160,] -0.969406870 0.5169782861 -0.0530161888 -0.047979551
## [161,] 0.655880718 1.4592848861 -1.1984338560 1.494489006
## [162,] -1.052152140 -0.3942984941 -0.5835206404 -0.365691128
## [163,] -0.198422354 -2.4027880287 0.2199424464 -0.009131037
## [164,] -0.866074733 0.4276110049 -0.1121833304 -0.215613772
## [165,] 0.675019418 0.3745707730 -1.8374436293 0.972257923
## [166,] 0.628645183 -1.4678549959 -0.0810003790 0.957704120
## [167,] 0.915856252 1.2083027455 -1.3626640042 1.060713792
## [168,] -1.026299834 -0.0536874444 -0.3849069210 -0.240723350
## [169,] 0.142791800 -0.4864577553 1.3248292074 0.454224690
## [170,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [171,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [172,] 2.805324565 -0.1857046418 -0.2642717824 0.431480320
## [173,] -0.070486344 -0.9792102723 1.0487705693 0.488816383
## [174,] -0.663931846 1.0296359635 0.2288381769 -0.186321580
## [175,] 2.352736343 -0.2275794585 -0.2598911857 0.966460288
## [176,] -0.945222724 0.2988465531 -0.1828216316 -0.177900756
## [177,] -1.064906265 -0.5087286154 -0.6499852562 -0.402691984
## [178,] -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## [179,] -0.841709082 1.4937985069 0.5131455209 0.244822996
## [180,] 0.092394215 0.9695725098 0.1450570150 -1.140131503
## [181,] -1.010510802 -0.1619551432 -0.4495772422 -0.309844189
## [182,] -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## [183,] -1.046137539 -0.2534042938 -0.5010639731 -0.308267890
## [184,] -0.990722301 -0.3810358893 -0.5796590064 -0.434818916
## [185,] 0.918110825 -0.3190676064 1.3735677099 -0.418251785
## [186,] -0.985417223 0.2343303615 -0.2181797885 -0.158345987
## [187,] -0.723057710 1.9661212539 0.7832556823 0.316716027
## [188,] 0.080389515 -2.1750781991 0.3359635504 -0.245851765
## [189,] -0.983485098 -0.0444438107 -0.3822154791 -0.288903324
## [190,] -0.663587790 1.1413867707 0.2945226647 -0.135355514
## [191,] 0.035763975 -2.0171979934 0.4316525661 -0.118604217
## [192,] -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## [193,] -0.904063665 0.4752475176 -0.0817399805 -0.147187719
## [194,] -0.951599786 0.2416314925 -0.2160539395 -0.196401184
## [195,] -1.038123204 -0.1679166171 -0.4513130272 -0.278771597
## [196,] 0.557036252 0.5724514462 -1.7135346287 1.207732372
## [197,] 0.902107564 1.4540526970 -0.4196281764 -0.359180401
## [198,] -0.085101979 -1.0940422907 0.9821889342 0.453910308
## [199,] -0.008021331 -1.1332389640 0.9542029877 0.341493845
## [200,] -0.378687788 0.8120283889 0.0826121866 -0.635693481
## [201,] -0.599817166 1.7135373771 0.6268457439 0.049648766
## [202,] -0.026241670 -0.8579813915 1.1172147602 0.490380519
## [203,] -0.541975130 2.1727314849 0.8931332776 0.189971325
## [204,] -0.875726341 0.3138507121 -0.1784529143 -0.256105930
## [205,] 0.171281245 -0.1452773513 1.5236087040 0.576224861
## [206,] 1.576021360 -0.5627857815 -0.4072117308 1.763477798
## [207,] 0.923765970 -0.5970379844 1.2097660577 -0.552998685
## [208,] 7.783122743 1.1123471486 0.1799708403 -5.067393551
## [209,] 0.300498078 0.3851647248 1.8272144666 0.661905062
## [210,] -0.858188104 -1.1899959107 -1.0637990199 -0.969110629
## [211,] 0.053228880 1.7428524577 0.6022350001 -0.736585590
## [212,] -1.011757819 0.8428643613 0.1413101027 0.153738226
## [213,] -0.906960350 0.6421369169 0.0165722159 -0.066898188
## [214,] -0.672282725 -0.4239618153 -0.6253039538 -0.844516306
## [215,] -1.010925472 0.0054701190 -0.3511090202 -0.232347699
## [216,] 1.933332924 1.1843972844 2.1925100067 -0.970132055
## [217,] 1.565398897 -0.1793191374 1.4142578648 -1.146653382
## [218,] -1.107413754 -0.0153615482 -0.3571745161 -0.123768194
## [219,] 0.162439072 -0.1471863626 1.5230528628 0.586175073
## [220,] 0.880591976 1.0331744552 -1.4633750945 1.023367281
## [221,] 1.028205947 1.2681731193 2.2997685989 0.176802071
## [222,] 0.042129017 0.0501919392 1.6468155894 0.824267999
## [223,] -0.089306659 -0.8260077929 -1.6967138668 -0.193564097
## [224,] 0.133484249 -0.4884672409 1.3242441113 0.464698597
## [225,] 0.015297746 2.4351953850 0.2140847545 1.177967084
## [226,] -0.990811408 0.1773275026 -0.2513503103 -0.177952460
## [227,] -1.046911665 -0.5048436099 -0.6488540705 -0.422941538
## [228,] -1.045775078 -0.3370834335 -0.5502883325 -0.347190700
## [229,] 0.594006912 0.7479481421 -1.6127162708 1.243158667
## [230,] -0.957632792 0.2961672390 -0.1836017597 -0.163935546
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## [471,] -0.737562916 0.6787095545 0.0272209644 -0.257523300
## [472,] -0.954364257 1.3577999071 0.4404008739 0.320242078
## [473,] 1.295032960 1.7927107626 -1.0433451356 0.865110929
## [474,] 0.147104525 -1.0997475377 0.9639545889 0.166928724
## [475,] -0.886348518 1.0932930825 0.2805193655 0.115320000
## [476,] 0.828746136 0.9103044945 -1.5322971138 1.030356835
## [477,] -0.844289504 0.6556674532 0.0205118628 -0.137422497
## [478,] -0.977541024 0.2918690833 -0.1848532411 -0.141532557
## [479,] -0.716152542 0.1807876533 -0.2669159935 -0.512706234
## [480,] 1.858181219 -0.8927357559 -0.6192944612 1.266223349
## [481,] 1.818545801 0.1545261929 1.5943284642 -1.303139759
## [482,] 0.295813503 -0.2300675603 1.4657742552 0.384733873
## [483,] -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## [484,] 0.618687125 -0.9979336016 0.9935994563 -0.363749244
## [485,] -0.871315208 0.5381561207 -0.0468499003 -0.158363362
## [486,] 0.024588903 -1.0145219402 1.0219158085 0.356150366
## [487,] 0.168484098 -2.2118969811 0.3086699676 -0.370662352
## [488,] -0.970730973 0.0699863105 -0.3157508632 -0.251902468
## [489,] 0.627619931 0.4201755618 -1.8075918505 1.051273794
## [490,] -0.346802476 1.0981036921 0.2487737262 -0.543191341
## [491,] 0.598958458 0.0231197543 -2.0392135910 0.903790591
## [492,] -1.035450844 -0.2231779219 -0.4839764657 -0.307455456
## [493,] -0.933119902 -0.2010848336 -0.4775436855 -0.422609782
## [494,] -0.476736169 2.1309782101 0.8644029329 0.090880464
## [495,] 0.021367562 1.9897997448 -0.0481851196 0.965723695
## [496,] 0.760369327 -1.1348594275 0.9040116664 -0.600215905
## [497,] -1.003049274 0.0630088408 -0.3177824728 -0.215534269
## [498,] -0.384373271 3.2118462101 1.4940062621 0.474799055
## [499,] -0.854067028 1.4911304459 0.5123686693 0.258729552
## [500,] 0.858634719 0.7492426033 -1.6289125316 0.919692973
## [501,] 0.062617651 -1.9555620645 0.4661720854 -0.123146385
## [502,] -0.001128184 -0.9083976926 1.0859620273 0.436443372
## [503,] -0.964424525 0.4063774405 -0.1183658456 -0.104939485
## [504,] -0.743387084 0.3982608109 -0.1373023062 -0.379352380
## [505,] 0.412967328 -0.0930977091 1.5388016986 0.304252402
## [506,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [507,] 2.214952369 -0.7040329041 -0.5312040706 0.916097420
## [508,] 0.017978214 -2.3560674890 0.2335459300 -0.252649381
## [509,] 1.445664747 -2.1683604967 -1.3428941655 1.184805303
## [510,] 1.534375252 1.7885461213 -1.0611309074 0.570099349
## [511,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [512,] 1.073734558 2.1358006292 -0.8274365011 1.293877196
## [513,] -0.100648369 -1.2090752577 0.9155487896 0.420051625
## [514,] 0.059201877 -1.4537551579 0.7614402290 0.111786995
## [515,] -1.028264174 -0.2216263311 -0.4835246935 -0.315542709
## [516,] 0.628989240 -1.3561041888 -0.0153158913 1.008670186
## [517,] -0.201650787 0.1243529781 -0.3330674094 -1.168711535
## [518,] 0.826856211 -0.5316493414 0.4567625403 1.145480593
## [519,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [520,] 2.051681755 2.4586144052 -0.7002974230 0.244733868
## [521,] 0.710618450 1.7731052982 0.5778973011 -1.527707770
## [522,] 0.620806875 1.1446020526 -1.3812115495 1.392736652
## [523,] -0.649575756 1.3119267355 0.3938977856 -0.074093581
## [524,] -0.944242677 0.6340877215 0.0142285551 -0.024943905
## [525,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [526,] -0.150634288 0.5820734632 -0.0672089460 -1.020708111
## [527,] -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## [528,] -0.892725581 1.0360780218 0.2472870575 0.096819572
## [529,] 0.398058344 -0.1521547982 1.5050330526 0.295353056
## [530,] -0.423827822 0.4672531492 -0.1172140079 -0.738956530
## [531,] -0.690140229 2.5874489786 1.1464706851 0.562116364
## [532,] -0.907820490 0.3627598990 -0.1476390034 -0.194313352
## [533,] -1.055564909 -0.3950353055 -0.5837351756 -0.361850695
## [534,] -1.010701235 -0.0224006000 -0.3675106389 -0.245438346
## [535,] -0.104093527 -1.4890103767 0.7511750695 0.295545414
## [536,] 0.515229071 0.0406569652 1.6108929883 0.240529183
## [537,] 6.863676311 2.2690746189 -1.1200948062 -5.735151130
## [538,] 1.400456943 0.5870298479 -1.7590093736 0.181590361
## [539,] -1.024816185 -0.2767201788 -0.5161393741 -0.345099393
## [540,] -0.595529231 -0.5190673836 -0.6861418958 -0.982241237
## [541,] -0.400223903 2.0916588243 0.8363812565 -0.020896392
## [542,] 0.951488913 0.3784218357 -1.8528954919 0.635466626
## [543,] -0.685036850 -0.5383919366 -0.6917685696 -0.881517162
## [544,] -1.019455804 -0.3314011441 -0.5486338368 -0.376808117
## [545,] -1.055306779 -0.3949795758 -0.5837189490 -0.362141172
## [546,] 2.377351952 -1.1207850191 0.8086706795 -2.573886970
## [547,] -0.361777480 0.4806497197 -0.1133133674 -0.808782579
## [548,] 1.393895544 -1.9980630309 -1.2394463610 1.326510863
## [549,] 0.525150940 0.2863761430 -1.8796961683 1.115230232
## [550,] -0.554729254 2.0583013637 0.8266686618 0.152970469
## [551,] -0.767697146 1.5656158294 0.5506295269 0.187213031
## [552,] -0.886348518 1.0932930825 0.2805193655 0.115320000
## [553,] 1.964607033 1.9372707439 -1.0012540266 0.111630608
## [554,] -0.904066670 0.9777912355 0.2137426984 0.083905228
## [555,] 4.140273072 -0.6233887932 -0.6071621510 -1.404550452
## [556,] -0.717413457 0.6272215278 -0.0043438198 -0.305874364
## [557,] 1.496049864 -1.1942723936 -0.7733846673 1.571027950
## [558,] -0.239887753 0.1465707212 -1.1152140373 0.438065875
## [559,] -1.003565532 0.0628973813 -0.3178149261 -0.214953316
## [560,] -0.695473102 0.8553114675 0.1283611251 -0.227857654
## [561,] 0.113486911 0.0655979953 1.6513013259 0.743968043
## [562,] -0.672774020 1.0277269522 0.2282823357 -0.176371368
## [563,] 1.680024423 -0.8804690868 0.9946549267 -1.609438999
## [564,] 1.969285136 -0.7570720703 -0.5466473302 1.192549919
## [565,] -0.315417761 1.4399091800 0.4477352267 -0.424449254
## [566,] -0.964217103 0.2389074338 -0.2168470957 -0.182202755
## [567,] -0.773902181 1.5642761724 0.5502394628 0.194195636
## [568,] -1.050739105 -0.3381551591 -0.5506003837 -0.341604616
## [569,] 4.267814319 0.5209124195 0.0574840074 -1.034541892
## [570,] -0.038530417 -0.9723110385 1.0507793991 0.452855968
## [571,] -0.959908973 0.4631906041 -0.0852505569 -0.084344275
## [572,] 0.106777812 -2.1135427445 0.3704538149 -0.249870238
## [573,] -1.070887148 -0.4541816157 -0.6175297999 -0.370285000
## [574,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [575,] -0.786656305 1.4498460511 0.4837748470 0.157194780
## [576,] -0.435684996 0.2413401522 -0.2492850987 -0.828319973
## [577,] -1.031796848 -0.2782272929 -0.5165781961 -0.337243963
## [578,] 0.110906488 -0.7725330585 1.1586676678 0.361722550
## [579,] -0.784751975 0.0543006186 -0.3368911858 -0.486863646
## [580,] -0.083240468 -1.0936403936 0.9823059535 0.451815527
## [581,] 2.466630825 -0.3197741702 1.2739229903 -2.314880978
## [582,] 0.579363483 -0.4836551365 -2.3359282481 0.694751503
## [583,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [584,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [585,] -0.885291934 0.2280281211 -0.2283013761 -0.283856572
## [586,] 0.391678276 0.2931738592 1.7672834236 0.507945575
## [587,] 6.857299249 2.2118595583 -1.1533271141 -5.753651558
## [588,] -0.058732173 0.8252680362 0.0698939709 -1.021420270
## [589,] 4.591895143 -0.3583695147 -0.4802777633 -1.835736725
## [590,] -0.913988715 -0.0294396517 -0.3778467618 -0.367108498
## [591,] -0.970801588 0.3491623799 -0.1515981535 -0.123439913
## [592,] 0.060668911 2.7495474821 1.1936684346 -0.282778822
## [593,] -0.913503430 -0.4760409833 -0.6404676935 -0.573067542
## [594,] 0.011625941 -0.7939675713 1.1524266431 0.473444228
## [595,] -0.486701495 -0.2163803329 -0.5151435620 -0.976323397
## [596,] -0.201522375 0.4898833233 -0.9158137147 0.548952532
## [597,] -0.030076997 -2.2547660068 0.2961879182 -0.147218997
## [598,] -1.073762336 -1.0690232568 -0.9788562686 -0.649492317
## [599,] -0.938501605 0.4678124209 -0.0839048359 -0.108434262
## [600,] -1.022180461 -0.1086363412 -0.4174793966 -0.271035553
## [601,] 0.771736622 0.3752278537 1.7911748463 0.080261028
## [602,] -1.082621690 -1.3685539190 -1.1544047104 -0.776379148
## [603,] -0.991536156 0.1771710306 -0.2513958698 -0.177136892
## [604,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [605,] -0.950119142 0.5211424761 -0.0518037137 -0.069684280
## [606,] 0.942897157 -0.4253928025 1.3094629815 -0.497497401
## [607,] -0.916959019 0.9191695350 0.1801008232 0.072736535
## [608,] 0.493317750 0.0003120929 -2.0458544313 1.022669439
## [609,] 1.377765637 -0.1639905980 1.4352941963 -0.909830642
## [610,] -1.068319034 -0.5094654268 -0.6501997915 -0.398851551
## [611,] 0.951681199 0.5815923917 1.9009809039 -0.045203065
## [612,] 0.721112588 -0.6382366167 0.4008680858 1.225960326
## [613,] -0.958995120 0.4075496405 -0.1180245395 -0.111049264
## [614,] -0.995895167 -0.0471231248 -0.3829956072 -0.274938114
## [615,] -0.863270160 1.3216287153 0.4132958480 0.192056100
## [616,] 0.152781454 0.7441407806 2.0477486367 1.007868808
## [617,] 0.288776122 0.6059870250 1.9578033140 0.777802403
## [618,] -1.055875161 -0.3951022883 -0.5837546788 -0.361501565
## [619,] -0.154315904 -2.2257507272 0.3212093779 0.018265263
## [620,] 2.555909698 0.4812366788 1.7391753012 -2.055874986
## [621,] 1.374501807 -1.4997057412 -0.9451826323 1.579424450
## [622,] 0.474767141 -1.4198735389 0.7547322762 -0.381530563
## [623,] -0.709603452 0.2938781176 -0.2008414417 -0.468722773
## [624,] -1.019922772 0.0035276162 -0.3516746131 -0.222222922
## [625,] -1.017440758 0.0040634791 -0.3515185874 -0.225015964
## [626,] -0.133206306 -1.4952957797 0.7493449671 0.328306399
## [627,] -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## [628,] -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## [629,] 1.552283925 1.6807360493 -1.1256679827 0.498593253
## [630,] -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## [631,] -1.009426336 0.0057937801 -0.3510147807 -0.234034697
## [632,] -0.856803991 0.8204803841 0.1182194599 -0.046309928
## [633,] 0.293242383 0.3277599687 1.7939269256 0.644393371
## [634,] -0.035567539 -0.7483183059 1.1822913721 0.552228276
## [635,] 0.557088374 0.5724626993 -1.7135313522 1.207673719
## [636,] 0.149998204 -0.7640932190 1.1611250713 0.317732140
## [637,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [638,] 0.182436410 -0.7012515988 1.1959956482 0.306905627
## [639,] 0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## [640,] 0.384432832 -1.1165091774 -2.6955386055 0.642450851
## [641,] -1.008099402 0.1177567890 -0.2852685068 -0.184174676
## [642,] -0.972663098 0.3487604828 -0.1517151727 -0.121345131
## [643,] -1.018134881 0.7856493007 0.1080777947 0.135237798
## [644,] -0.129741415 -1.4945477152 0.7495627788 0.324407312
## [645,] -0.856803991 0.8204803841 0.1182194599 -0.046309928
## [646,] 0.528400872 -0.5148818937 1.2834067033 -0.031059397
## [647,] -1.003152277 0.0629866024 -0.3177889479 -0.215418357
## [648,] -0.718431729 0.8503547364 0.1269178881 -0.202022016
## [649,] -0.913337412 0.5849218563 -0.0166600920 -0.085398616
## [650,] 0.085370444 -2.1181645613 0.3691080939 -0.225780251
## [651,] -0.972438860 0.3208897639 -0.1681167914 -0.134435778
## [652,] -0.095994593 -1.2080705149 0.9158413376 0.414814671
## [653,] 0.932975224 0.7094543375 -1.6570707304 0.810360028
## [654,] -0.912581690 1.0317911193 0.2460388526 0.119163907
## [655,] -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## [656,] 1.150931821 0.6804485484 1.9463377286 -0.243745737
## [657,] -0.987157412 0.1222781315 -0.2839520407 -0.207740967
## [658,] -1.024511943 0.7284342401 0.0748454868 0.116737370
## [659,] -0.014020532 -0.9670193932 1.0523201521 0.425274679
## [660,] -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## [661,] 0.741663353 -1.0069974816 -2.6540399679 0.255347188
## [662,] 1.476918676 -1.3659175755 -0.8730815910 1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,] 2.482590756 0.1913237442 -0.0219082027 1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,] 1.777909122 -0.4633602706 -0.3616891289 1.561967520
## [672,] 0.575960104 0.8278092592 -1.5646035940 1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677 0.9775233041 0.2136646856 0.085301749
## [675,] 0.597246238 0.8603240333 -1.5468497792 1.290866650
## [676,] -0.678750309 0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416 2.8090080902 1.2772740678 0.674173273
## [679,] 1.448480112 -1.7070869943 -1.0718578891 1.393469238
## [680,] 0.249972874 -1.5242445278 0.7077697138 -0.154243300
## [681,] 0.262235704 0.0418743610 1.6278206191 0.550902494
## [682,] -0.110195557 -1.4903277955 0.7507914806 0.302412107
## [683,] 1.991958015 0.4711569300 1.7693867405 -1.369899663
## [684,] -0.612122816 1.5433658179 0.5275778906 -0.013533383
## [685,] 1.593931448 -0.8381103369 -0.5702430064 1.614940254
## [686,] -0.830295788 0.9378799892 0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,] 0.286865320 0.2705449081 1.7606946177 0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,] 0.088150689 -0.1073868437 1.5512143381 0.695449364
## [691,] 1.546048265 -0.6809334511 -0.4747587744 1.745853671
## [692,] -0.442495047 0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274 0.0630088408 -0.3177824728 -0.215534269
## [695,] 0.610906330 0.2846665856 1.7482332202 0.235568806
## [696,] -0.994346913 0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766 1.2674836128 0.3809574109 0.157554335
## [698,] 1.678284518 -0.5965455906 -0.4336146414 1.622723132
## [699,] 1.387203810 -1.3852868731 -0.8787212930 1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,] 2.591000816 1.1639797750 0.5430410319 1.314577051
## [703,] 0.141071518 -1.0452117911 0.9964067687 0.199394362
## [704,] -0.958409837 0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972 0.8846308877 0.360120609
## [706,] -0.957976849 0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772 0.0035276162 -0.3516746131 -0.222222922
## [708,] 1.040582830 -0.0946382622 0.7000179410 1.084707607
## [709,] -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## [710,] 0.152449418 -1.3777848985 0.8001334335 0.032530955
## [711,] 0.814167311 0.4046125825 -1.8286964431 0.815673010
## [712,] -0.195145312 0.5470983840 -0.8825814068 0.567452960
plot(Temp2_pca$x,xlim=xlim,ylim=xlim)
Temp2_pca$rotation[,1]
## Sex Age Fare Embarked
## 0.44571001 0.09242234 0.65697225 -0.60098933
Temp2_pca$rotation
## PC1 PC2 PC3 PC4
## Sex 0.44571001 -0.5293273 0.64187639 0.3303784
## Age 0.09242234 0.8292140 0.48163361 0.2681255
## Fare 0.65697225 0.1418393 0.04129893 -0.7392993
## Embarked -0.60098933 -0.1099922 0.59524631 -0.5219151
plot(Temp2[,-1])
Temp2_pca$x
## PC1 PC2 PC3 PC4
## [1,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [2,] 2.328844131 0.1022918285 -0.0644045317 1.147406212
## [3,] -0.076863406 -1.0364253330 1.0155382614 0.470315955
## [4,] 0.541154997 -0.4004517724 1.3498713191 0.005941459
## [5,] -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## [6,] -0.278861772 1.7828311382 0.6470218066 -0.311526470
## [7,] -0.992543997 -1.2748413981 -1.1050763987 -0.843594832
## [8,] -0.030671121 -0.9706142289 1.0512734542 0.444011801
## [9,] 1.664344689 -1.3812908595 -0.8941309506 1.278937145
## [10,] -0.108260428 -2.2716456857 0.2912731112 -0.059238176
## [11,] 0.358340114 0.8443588327 2.0935020004 0.802227620
## [12,] -1.039398015 -0.2798683728 -0.5170560246 -0.328690272
## [13,] -0.630009991 0.8694448494 0.1324763008 -0.301524135
## [14,] -0.154266787 -1.7231957561 0.6166953333 0.249299556
## [15,] 0.208282705 0.6444468869 1.9855747253 0.894059299
## [16,] -0.121191971 -1.1120830961 -1.8628754064 -0.286066237
## [17,] 0.080053345 -0.7233559402 1.1895595915 0.422118607
## [18,] -0.720981351 0.6264512250 -0.0045681066 -0.301859366
## [19,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [20,] 0.625733012 -1.5243219921 -0.1140148752 0.935304605
## [21,] -0.647725138 0.2513992845 -0.2297830451 -0.564031854
## [22,] -0.028458129 -2.0310634439 0.4276154032 -0.046334256
## [23,] 0.290832573 -0.2869811981 1.4326297117 0.364662359
## [24,] 2.118171868 0.3460076983 -0.3513946758 -3.907620912
## [25,] 0.875161156 1.1995167387 -1.3652222002 1.106508508
## [26,] -0.715648479 2.3585887361 1.0135414535 0.488114652
## [27,] 1.474364633 0.6588246642 -1.7215319207 0.124097704
## [28,] -0.353680136 1.0966188162 0.2483413792 -0.535451822
## [29,] -1.033020953 -0.2226533122 -0.4838237166 -0.310189844
## [30,] -0.002848466 -1.4671517284 0.7575395885 0.181613043
## [31,] 1.430674269 -1.4317399327 -0.9088200604 1.541889474
## [32,] 0.031651073 -0.2312615472 1.4819997708 0.707675872
## [33,] 0.091775301 -0.9441782404 1.0589707441 0.306221266
## [34,] 1.737017034 -1.9798219080 -1.2507083116 0.914715217
## [35,] 0.649379751 -1.2958636466 0.0187973373 1.011401099
## [36,] -0.005330479 -1.4676875913 0.7573835629 0.184406085
## [37,] -0.729676286 -0.9388973610 -0.9243947250 -1.011020158
## [38,] -1.036123470 -0.2233231407 -0.4840187487 -0.306698542
## [39,] 2.466575808 0.7462487722 0.3053993550 1.274857785
## [40,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [41,] 1.459736803 2.7216822690 -0.5076885621 1.090593468
## [42,] -0.076792792 -1.3156014023 0.8513855516 0.341853400
## [43,] 0.547522780 0.4866401084 -1.7633798140 1.179923077
## [44,] 0.035247891 -2.1848242042 0.3331258345 -0.195053315
## [45,] -0.614660418 -0.6907125655 -0.7858388195 -1.037742521
## [46,] 0.506071875 0.1147422142 -1.9793898155 1.059670295
## [47,] 0.056057955 1.3525954097 0.3725928346 -0.919505513
## [48,] -0.895091155 -1.1421249580 -1.0332874086 -0.901906532
## [49,] -0.025776293 -0.8578809172 1.1172440150 0.489856824
## [50,] -1.044431067 -0.3367932638 -0.5502038446 -0.348703132
## [51,] -0.134256967 -1.5513608787 0.7164474901 0.303812103
## [52,] -0.993534474 0.0650630709 -0.3171843486 -0.226241395
## [53,] -0.932468599 0.4132766744 -0.1163570157 -0.140899900
## [54,] 0.343048387 -1.5041496720 0.7136206745 -0.258982373
## [55,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [56,] 0.621242869 0.3629605012 -1.8408241584 1.032773366
## [57,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [58,] -1.012476731 0.0051352047 -0.3512065362 -0.230602048
## [59,] -0.901655367 -1.3205494547 -1.1377756838 -0.975914620
## [60,] 0.005110655 -0.7953742112 1.1520170759 0.480775963
## [61,] -1.014854325 -0.1628929032 -0.4498502870 -0.304956365
## [62,] -0.964009855 0.2389521784 -0.2168340676 -0.182435974
## [63,] -0.503768344 0.2824793282 -0.2207335593 -0.726028287
## [64,] -0.102301041 -1.5444616449 0.7184563199 0.267851688
## [65,] 0.066125823 -0.6146863442 1.2543469319 0.489144664
## [66,] -0.738211213 -0.4381956715 -0.6294483843 -0.770326129
## [67,] 3.069503611 -0.5246444689 1.1148325103 -3.147361192
## [68,] -1.013889766 -0.0510081303 -0.3841267929 -0.254688560
## [69,] -0.982004454 0.2350671729 -0.2179652533 -0.162186420
## [70,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [71,] -0.214309508 1.3500617657 0.3884282861 -0.589580909
## [72,] -0.845699534 0.0969804002 -0.3078910727 -0.392601955
## [73,] -0.800620638 1.9493755407 0.7783798817 0.403998588
## [74,] 1.158894058 2.9917603749 -0.3296117147 1.583195391
## [75,] 1.209014909 0.3223447643 -1.9023696200 0.294316071
## [76,] 0.161234875 -0.5383141877 1.2931571557 0.407793843
## [77,] -0.727358414 0.5692361643 -0.0378004145 -0.320359794
## [78,] -0.064471655 -0.9220734477 1.0819800975 0.507724595
## [79,] -0.173778840 -0.0371443017 -0.4298095980 -1.277106050
## [80,] -0.948998041 0.4655462570 -0.0845646682 -0.096622488
## [81,] -0.932539213 0.6924527437 0.0477956940 -0.012437345
## [82,] -0.990295149 0.1774389620 -0.2513178570 -0.178533413
## [83,] -0.112161487 -1.3232374475 0.8491621866 0.381654248
## [84,] -0.926524525 0.7495895684 0.0810052222 0.006470867
## [85,] -0.321794824 1.3826941194 0.4145029188 -0.442949682
## [86,] 1.473730145 -1.3945251058 -0.8896977450 1.506276452
## [87,] -1.026643890 -0.1654382516 -0.4505914087 -0.291689416
## [88,] -0.091546650 -1.3746250000 0.8176266572 0.332779489
## [89,] 1.489723682 -1.2514764691 -0.8066137767 1.552470265
## [90,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [91,] 0.050371589 2.7498782185 0.3968624480 1.279719438
## [92,] -0.821294068 0.2697642906 -0.2078625945 -0.343035886
## [93,] 3.500861199 0.8729890093 -1.7254669726 -2.259051431
## [94,] 0.059862195 -2.3470248039 0.2361788623 -0.299781963
## [95,] -0.220781974 -0.0472922039 -0.4327643331 -1.224212819
## [96,] 0.856496849 0.7767001720 -1.6126312086 0.934937055
## [97,] 0.027568597 -0.6509299197 1.2355074129 0.519695298
## [98,] 0.036664218 1.8509526994 0.6668565633 -0.666591926
## [99,] 0.492096651 -0.4466576443 -2.3085826307 0.818630611
## [100,] -1.025161831 -0.0534417513 -0.3848353832 -0.242003960
## [101,] -0.893312280 1.1476278804 0.3129130357 0.148833028
## [102,] 0.584492113 0.7458939120 -1.6133143950 1.253865794
## [103,] -1.051808084 -0.2825476869 -0.5178361527 -0.314725062
## [104,] 0.138651104 0.1827074307 1.7185460698 0.767003689
## [105,] 0.166579768 -0.8163515486 1.1293360004 0.273396074
## [106,] -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## [107,] 0.609453478 0.1929004015 -1.9400595584 0.969010264
## [108,] 0.106324917 -1.3877431053 0.7972339315 0.084435450
## [109,] -0.371914372 0.8134907585 0.0830379805 -0.643315693
## [110,] -1.050427438 -0.5056026596 -0.6490750808 -0.418985194
## [111,] 1.411988553 0.4220047153 -1.8567787569 0.091583837
## [112,] -0.104543417 -1.2657544555 0.8824725073 0.398758155
## [113,] 0.008732262 -1.1296218900 0.9552561607 0.322640812
## [114,] -0.290457192 -0.1993767184 -1.3153815378 0.340912606
## [115,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [116,] -0.689606114 -0.2601871186 -0.5278986563 -0.747992218
## [117,] -0.997913218 0.1199559700 -0.2846281777 -0.195637320
## [118,] 0.142972844 -1.9382135057 0.4712234148 -0.213571117
## [119,] -0.711415758 0.7122738159 0.0452803553 -0.274108724
## [120,] -0.837672804 0.9921255660 0.2179163837 0.009191356
## [121,] -0.786174026 1.5057884376 0.5166365941 0.182328683
## [122,] 0.625789110 -1.1080768203 0.9283830454 -0.423094436
## [123,] -0.813012301 1.7512662798 0.6626909065 0.328074922
## [124,] -0.828623295 0.9103219462 0.1692381139 -0.039507101
## [125,] 1.363011889 1.9190638316 -0.9734089498 0.839966602
## [126,] 0.628437935 -1.4678997405 -0.0810134072 0.957937339
## [127,] -0.975627392 0.2922822335 -0.1847329454 -0.143685992
## [128,] -0.786447467 1.1148615610 0.2867993966 0.002900062
## [129,] 0.109524253 -0.2144488512 1.4868950745 0.620044181
## [130,] -1.004548410 0.0626851796 -0.3178767123 -0.213847271
## [131,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [132,] -0.767938660 -1.2821877249 -1.1237885725 -1.122022726
## [133,] -0.954730098 -0.8758095964 -0.8728793137 -0.706410971
## [134,] 0.292191896 0.1041801184 1.6625351704 0.542869023
## [135,] -0.387165823 0.3076536277 -0.2134036318 -0.857242604
## [136,] -0.462102217 2.1341376573 0.8653228600 0.074412689
## [137,] -0.108437846 -0.9976529748 -1.7964107906 -0.249065381
## [138,] -0.196474743 -2.4582058055 0.1872334484 -0.036999327
## [139,] -1.034572211 -0.2229882265 -0.4839212327 -0.308444193
## [140,] 1.014114107 2.1229286683 -0.8311843925 1.360968857
## [141,] -1.054582031 -0.3948231038 -0.5836733895 -0.362956740
## [142,] 1.877062338 0.6748120111 0.3011724864 1.963921497
## [143,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [144,] -1.037266068 0.6140041188 0.0083808710 0.079736514
## [145,] -0.819925729 -0.8467055469 -0.8644051723 -0.858108061
## [146,] -0.776470582 -1.2840297533 -1.1243249106 -1.112421644
## [147,] -0.042176813 -2.2573783381 0.2954272933 -0.133602918
## [148,] -0.650385190 1.2000754541 0.3281840430 -0.124535951
## [149,] -0.047950783 1.0255835534 -0.6106769508 0.607226009
## [150,] -0.939278650 0.6351594471 0.0145406064 -0.030529989
## [151,] 0.024380066 -0.6795374501 1.2188912589 0.510445084
## [152,] -0.984345239 -0.3238208286 -0.5464266984 -0.416318488
## [153,] -0.122381475 -1.4371204529 0.7828568729 0.341801696
## [154,] -0.925047347 -1.2044307154 -1.0680019599 -0.893873062
## [155,] 1.826492899 0.3288645715 0.1010049859 1.866768227
## [156,] 3.390087901 1.4481779364 0.6589365139 0.466707308
## [157,] -0.894706997 0.9798119742 0.2143310710 0.073372667
## [158,] -0.026636433 -1.1372579352 0.9530327956 0.362441660
## [159,] -0.970386917 0.1817371177 -0.2500663755 -0.200936402
## [160,] -0.969406870 0.5169782861 -0.0530161888 -0.047979551
## [161,] 0.655880718 1.4592848861 -1.1984338560 1.494489006
## [162,] -1.052152140 -0.3942984941 -0.5835206404 -0.365691128
## [163,] -0.198422354 -2.4027880287 0.2199424464 -0.009131037
## [164,] -0.866074733 0.4276110049 -0.1121833304 -0.215613772
## [165,] 0.675019418 0.3745707730 -1.8374436293 0.972257923
## [166,] 0.628645183 -1.4678549959 -0.0810003790 0.957704120
## [167,] 0.915856252 1.2083027455 -1.3626640042 1.060713792
## [168,] -1.026299834 -0.0536874444 -0.3849069210 -0.240723350
## [169,] 0.142791800 -0.4864577553 1.3248292074 0.454224690
## [170,] -1.036571945 -0.1675817029 -0.4512155112 -0.280517248
## [171,] -0.914197553 0.3055448384 -0.1808713113 -0.212813780
## [172,] 2.805324565 -0.1857046418 -0.2642717824 0.431480320
## [173,] -0.070486344 -0.9792102723 1.0487705693 0.488816383
## [174,] -0.663931846 1.0296359635 0.2288381769 -0.186321580
## [175,] 2.352736343 -0.2275794585 -0.2598911857 0.966460288
## [176,] -0.945222724 0.2988465531 -0.1828216316 -0.177900756
## [177,] -1.064906265 -0.5087286154 -0.6499852562 -0.402691984
## [178,] -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## [179,] -0.841709082 1.4937985069 0.5131455209 0.244822996
## [180,] 0.092394215 0.9695725098 0.1450570150 -1.140131503
## [181,] -1.010510802 -0.1619551432 -0.4495772422 -0.309844189
## [182,] -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## [183,] -1.046137539 -0.2534042938 -0.5010639731 -0.308267890
## [184,] -0.990722301 -0.3810358893 -0.5796590064 -0.434818916
## [185,] 0.918110825 -0.3190676064 1.3735677099 -0.418251785
## [186,] -0.985417223 0.2343303615 -0.2181797885 -0.158345987
## [187,] -0.723057710 1.9661212539 0.7832556823 0.316716027
## [188,] 0.080389515 -2.1750781991 0.3359635504 -0.245851765
## [189,] -0.983485098 -0.0444438107 -0.3822154791 -0.288903324
## [190,] -0.663587790 1.1413867707 0.2945226647 -0.135355514
## [191,] 0.035763975 -2.0171979934 0.4316525661 -0.118604217
## [192,] -1.015370410 -0.3305191139 -0.5483770187 -0.381405464
## [193,] -0.904063665 0.4752475176 -0.0817399805 -0.147187719
## [194,] -0.951599786 0.2416314925 -0.2160539395 -0.196401184
## [195,] -1.038123204 -0.1679166171 -0.4513130272 -0.278771597
## [196,] 0.557036252 0.5724514462 -1.7135346287 1.207732372
## [197,] 0.902107564 1.4540526970 -0.4196281764 -0.359180401
## [198,] -0.085101979 -1.0940422907 0.9821889342 0.453910308
## [199,] -0.008021331 -1.1332389640 0.9542029877 0.341493845
## [200,] -0.378687788 0.8120283889 0.0826121866 -0.635693481
## [201,] -0.599817166 1.7135373771 0.6268457439 0.049648766
## [202,] -0.026241670 -0.8579813915 1.1172147602 0.490380519
## [203,] -0.541975130 2.1727314849 0.8931332776 0.189971325
## [204,] -0.875726341 0.3138507121 -0.1784529143 -0.256105930
## [205,] 0.171281245 -0.1452773513 1.5236087040 0.576224861
## [206,] 1.576021360 -0.5627857815 -0.4072117308 1.763477798
## [207,] 0.923765970 -0.5970379844 1.2097660577 -0.552998685
## [208,] 7.783122743 1.1123471486 0.1799708403 -5.067393551
## [209,] 0.300498078 0.3851647248 1.8272144666 0.661905062
## [210,] -0.858188104 -1.1899959107 -1.0637990199 -0.969110629
## [211,] 0.053228880 1.7428524577 0.6022350001 -0.736585590
## [212,] -1.011757819 0.8428643613 0.1413101027 0.153738226
## [213,] -0.906960350 0.6421369169 0.0165722159 -0.066898188
## [214,] -0.672282725 -0.4239618153 -0.6253039538 -0.844516306
## [215,] -1.010925472 0.0054701190 -0.3511090202 -0.232347699
## [216,] 1.933332924 1.1843972844 2.1925100067 -0.970132055
## [217,] 1.565398897 -0.1793191374 1.4142578648 -1.146653382
## [218,] -1.107413754 -0.0153615482 -0.3571745161 -0.123768194
## [219,] 0.162439072 -0.1471863626 1.5230528628 0.586175073
## [220,] 0.880591976 1.0331744552 -1.4633750945 1.023367281
## [221,] 1.028205947 1.2681731193 2.2997685989 0.176802071
## [222,] 0.042129017 0.0501919392 1.6468155894 0.824267999
## [223,] -0.089306659 -0.8260077929 -1.6967138668 -0.193564097
## [224,] 0.133484249 -0.4884672409 1.3242441113 0.464698597
## [225,] 0.015297746 2.4351953850 0.2140847545 1.177967084
## [226,] -0.990811408 0.1773275026 -0.2513503103 -0.177952460
## [227,] -1.046911665 -0.5048436099 -0.6488540705 -0.422941538
## [228,] -1.045775078 -0.3370834335 -0.5502883325 -0.347190700
## [229,] 0.594006912 0.7479481421 -1.6127162708 1.243158667
## [230,] -0.957632792 0.2961672390 -0.1836017597 -0.163935546
## [231,] -1.028557523 -0.1658514018 -0.4507117045 -0.289535981
## [232,] -0.837672804 0.9921255660 0.2179163837 0.009191356
## [233,] 0.666907557 -1.1245646321 0.1183934685 1.068706688
## [234,] 0.803320697 -0.8463949799 1.0708688462 -0.520166543
## [235,] 2.453348419 -0.9317548895 -0.6803750444 0.519444185
## [236,] 0.665415513 0.9308799347 -1.5097330575 1.239831506
## [237,] -0.078138217 -1.1483770887 0.9497952640 0.420397280
## [238,] -1.015803398 -0.0514212805 -0.3842470886 -0.252535125
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## [479,] -0.716152542 0.1807876533 -0.2669159935 -0.512706234
## [480,] 1.858181219 -0.8927357559 -0.6192944612 1.266223349
## [481,] 1.818545801 0.1545261929 1.5943284642 -1.303139759
## [482,] 0.295813503 -0.2300675603 1.4657742552 0.384733873
## [483,] -0.943742080 0.5783575367 -0.0185714058 -0.051183852
## [484,] 0.618687125 -0.9979336016 0.9935994563 -0.363749244
## [485,] -0.871315208 0.5381561207 -0.0468499003 -0.158363362
## [486,] 0.024588903 -1.0145219402 1.0219158085 0.356150366
## [487,] 0.168484098 -2.2118969811 0.3086699676 -0.370662352
## [488,] -0.970730973 0.0699863105 -0.3157508632 -0.251902468
## [489,] 0.627619931 0.4201755618 -1.8075918505 1.051273794
## [490,] -0.346802476 1.0981036921 0.2487737262 -0.543191341
## [491,] 0.598958458 0.0231197543 -2.0392135910 0.903790591
## [492,] -1.035450844 -0.2231779219 -0.4839764657 -0.307455456
## [493,] -0.933119902 -0.2010848336 -0.4775436855 -0.422609782
## [494,] -0.476736169 2.1309782101 0.8644029329 0.090880464
## [495,] 0.021367562 1.9897997448 -0.0481851196 0.965723695
## [496,] 0.760369327 -1.1348594275 0.9040116664 -0.600215905
## [497,] -1.003049274 0.0630088408 -0.3177824728 -0.215534269
## [498,] -0.384373271 3.2118462101 1.4940062621 0.474799055
## [499,] -0.854067028 1.4911304459 0.5123686693 0.258729552
## [500,] 0.858634719 0.7492426033 -1.6289125316 0.919692973
## [501,] 0.062617651 -1.9555620645 0.4661720854 -0.123146385
## [502,] -0.001128184 -0.9083976926 1.0859620273 0.436443372
## [503,] -0.964424525 0.4063774405 -0.1183658456 -0.104939485
## [504,] -0.743387084 0.3982608109 -0.1373023062 -0.379352380
## [505,] 0.412967328 -0.0930977091 1.5388016986 0.304252402
## [506,] -1.041827907 -0.2803929825 -0.5172087736 -0.325955884
## [507,] 2.214952369 -0.7040329041 -0.5312040706 0.916097420
## [508,] 0.017978214 -2.3560674890 0.2335459300 -0.252649381
## [509,] 1.445664747 -2.1683604967 -1.3428941655 1.184805303
## [510,] 1.534375252 1.7885461213 -1.0611309074 0.570099349
## [511,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [512,] 1.073734558 2.1358006292 -0.8274365011 1.293877196
## [513,] -0.100648369 -1.2090752577 0.9155487896 0.420051625
## [514,] 0.059201877 -1.4537551579 0.7614402290 0.111786995
## [515,] -1.028264174 -0.2216263311 -0.4835246935 -0.315542709
## [516,] 0.628989240 -1.3561041888 -0.0153158913 1.008670186
## [517,] -0.201650787 0.1243529781 -0.3330674094 -1.168711535
## [518,] 0.826856211 -0.5316493414 0.4567625403 1.145480593
## [519,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [520,] 2.051681755 2.4586144052 -0.7002974230 0.244733868
## [521,] 0.710618450 1.7731052982 0.5778973011 -1.527707770
## [522,] 0.620806875 1.1446020526 -1.3812115495 1.392736652
## [523,] -0.649575756 1.3119267355 0.3938977856 -0.074093581
## [524,] -0.944242677 0.6340877215 0.0142285551 -0.024943905
## [525,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [526,] -0.150634288 0.5820734632 -0.0672089460 -1.020708111
## [527,] -0.946082865 0.0194695352 -0.3470328509 -0.305315920
## [528,] -0.892725581 1.0360780218 0.2472870575 0.096819572
## [529,] 0.398058344 -0.1521547982 1.5050330526 0.295353056
## [530,] -0.423827822 0.4672531492 -0.1172140079 -0.738956530
## [531,] -0.690140229 2.5874489786 1.1464706851 0.562116364
## [532,] -0.907820490 0.3627598990 -0.1476390034 -0.194313352
## [533,] -1.055564909 -0.3950353055 -0.5837351756 -0.361850695
## [534,] -1.010701235 -0.0224006000 -0.3675106389 -0.245438346
## [535,] -0.104093527 -1.4890103767 0.7511750695 0.295545414
## [536,] 0.515229071 0.0406569652 1.6108929883 0.240529183
## [537,] 6.863676311 2.2690746189 -1.1200948062 -5.735151130
## [538,] 1.400456943 0.5870298479 -1.7590093736 0.181590361
## [539,] -1.024816185 -0.2767201788 -0.5161393741 -0.345099393
## [540,] -0.595529231 -0.5190673836 -0.6861418958 -0.982241237
## [541,] -0.400223903 2.0916588243 0.8363812565 -0.020896392
## [542,] 0.951488913 0.3784218357 -1.8528954919 0.635466626
## [543,] -0.685036850 -0.5383919366 -0.6917685696 -0.881517162
## [544,] -1.019455804 -0.3314011441 -0.5486338368 -0.376808117
## [545,] -1.055306779 -0.3949795758 -0.5837189490 -0.362141172
## [546,] 2.377351952 -1.1207850191 0.8086706795 -2.573886970
## [547,] -0.361777480 0.4806497197 -0.1133133674 -0.808782579
## [548,] 1.393895544 -1.9980630309 -1.2394463610 1.326510863
## [549,] 0.525150940 0.2863761430 -1.8796961683 1.115230232
## [550,] -0.554729254 2.0583013637 0.8266686618 0.152970469
## [551,] -0.767697146 1.5656158294 0.5506295269 0.187213031
## [552,] -0.886348518 1.0932930825 0.2805193655 0.115320000
## [553,] 1.964607033 1.9372707439 -1.0012540266 0.111630608
## [554,] -0.904066670 0.9777912355 0.2137426984 0.083905228
## [555,] 4.140273072 -0.6233887932 -0.6071621510 -1.404550452
## [556,] -0.717413457 0.6272215278 -0.0043438198 -0.305874364
## [557,] 1.496049864 -1.1942723936 -0.7733846673 1.571027950
## [558,] -0.239887753 0.1465707212 -1.1152140373 0.438065875
## [559,] -1.003565532 0.0628973813 -0.3178149261 -0.214953316
## [560,] -0.695473102 0.8553114675 0.1283611251 -0.227857654
## [561,] 0.113486911 0.0655979953 1.6513013259 0.743968043
## [562,] -0.672774020 1.0277269522 0.2282823357 -0.176371368
## [563,] 1.680024423 -0.8804690868 0.9946549267 -1.609438999
## [564,] 1.969285136 -0.7570720703 -0.5466473302 1.192549919
## [565,] -0.315417761 1.4399091800 0.4477352267 -0.424449254
## [566,] -0.964217103 0.2389074338 -0.2168470957 -0.182202755
## [567,] -0.773902181 1.5642761724 0.5502394628 0.194195636
## [568,] -1.050739105 -0.3381551591 -0.5506003837 -0.341604616
## [569,] 4.267814319 0.5209124195 0.0574840074 -1.034541892
## [570,] -0.038530417 -0.9723110385 1.0507793991 0.452855968
## [571,] -0.959908973 0.4631906041 -0.0852505569 -0.084344275
## [572,] 0.106777812 -2.1135427445 0.3704538149 -0.249870238
## [573,] -1.070887148 -0.4541816157 -0.6175297999 -0.370285000
## [574,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [575,] -0.786656305 1.4498460511 0.4837748470 0.157194780
## [576,] -0.435684996 0.2413401522 -0.2492850987 -0.828319973
## [577,] -1.031796848 -0.2782272929 -0.5165781961 -0.337243963
## [578,] 0.110906488 -0.7725330585 1.1586676678 0.361722550
## [579,] -0.784751975 0.0543006186 -0.3368911858 -0.486863646
## [580,] -0.083240468 -1.0936403936 0.9823059535 0.451815527
## [581,] 2.466630825 -0.3197741702 1.2739229903 -2.314880978
## [582,] 0.579363483 -0.4836551365 -2.3359282481 0.694751503
## [583,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [584,] -0.958836989 -0.0949605861 -0.4134974668 -0.342316776
## [585,] -0.885291934 0.2280281211 -0.2283013761 -0.283856572
## [586,] 0.391678276 0.2931738592 1.7672834236 0.507945575
## [587,] 6.857299249 2.2118595583 -1.1533271141 -5.753651558
## [588,] -0.058732173 0.8252680362 0.0698939709 -1.021420270
## [589,] 4.591895143 -0.3583695147 -0.4802777633 -1.835736725
## [590,] -0.913988715 -0.0294396517 -0.3778467618 -0.367108498
## [591,] -0.970801588 0.3491623799 -0.1515981535 -0.123439913
## [592,] 0.060668911 2.7495474821 1.1936684346 -0.282778822
## [593,] -0.913503430 -0.4760409833 -0.6404676935 -0.573067542
## [594,] 0.011625941 -0.7939675713 1.1524266431 0.473444228
## [595,] -0.486701495 -0.2163803329 -0.5151435620 -0.976323397
## [596,] -0.201522375 0.4898833233 -0.9158137147 0.548952532
## [597,] -0.030076997 -2.2547660068 0.2961879182 -0.147218997
## [598,] -1.073762336 -1.0690232568 -0.9788562686 -0.649492317
## [599,] -0.938501605 0.4678124209 -0.0839048359 -0.108434262
## [600,] -1.022180461 -0.1086363412 -0.4174793966 -0.271035553
## [601,] 0.771736622 0.3752278537 1.7911748463 0.080261028
## [602,] -1.082621690 -1.3685539190 -1.1544047104 -0.776379148
## [603,] -0.991536156 0.1771710306 -0.2513958698 -0.177136892
## [604,] -1.009337404 -0.3850548604 -0.5808291985 -0.413871101
## [605,] -0.950119142 0.5211424761 -0.0518037137 -0.069684280
## [606,] 0.942897157 -0.4253928025 1.3094629815 -0.497497401
## [607,] -0.916959019 0.9191695350 0.1801008232 0.072736535
## [608,] 0.493317750 0.0003120929 -2.0458544313 1.022669439
## [609,] 1.377765637 -0.1639905980 1.4352941963 -0.909830642
## [610,] -1.068319034 -0.5094654268 -0.6501997915 -0.398851551
## [611,] 0.951681199 0.5815923917 1.9009809039 -0.045203065
## [612,] 0.721112588 -0.6382366167 0.4008680858 1.225960326
## [613,] -0.958995120 0.4075496405 -0.1180245395 -0.111049264
## [614,] -0.995895167 -0.0471231248 -0.3829956072 -0.274938114
## [615,] -0.863270160 1.3216287153 0.4132958480 0.192056100
## [616,] 0.152781454 0.7441407806 2.0477486367 1.007868808
## [617,] 0.288776122 0.6059870250 1.9578033140 0.777802403
## [618,] -1.055875161 -0.3951022883 -0.5837546788 -0.361501565
## [619,] -0.154315904 -2.2257507272 0.3212093779 0.018265263
## [620,] 2.555909698 0.4812366788 1.7391753012 -2.055874986
## [621,] 1.374501807 -1.4997057412 -0.9451826323 1.579424450
## [622,] 0.474767141 -1.4198735389 0.7547322762 -0.381530563
## [623,] -0.709603452 0.2938781176 -0.2008414417 -0.468722773
## [624,] -1.019922772 0.0035276162 -0.3516746131 -0.222222922
## [625,] -1.017440758 0.0040634791 -0.3515185874 -0.225015964
## [626,] -0.133206306 -1.4952957797 0.7493449671 0.328306399
## [627,] -0.082929597 -0.7687927323 -1.6634815589 -0.175063669
## [628,] -1.005126093 -1.3333961158 -1.1386987707 -0.855112655
## [629,] 1.552283925 1.6807360493 -1.1256679827 0.498593253
## [630,] -0.842145536 -0.4606349272 -0.6359819570 -0.653367498
## [631,] -1.009426336 0.0057937801 -0.3510147807 -0.234034697
## [632,] -0.856803991 0.8204803841 0.1182194599 -0.046309928
## [633,] 0.293242383 0.3277599687 1.7939269256 0.644393371
## [634,] -0.035567539 -0.7483183059 1.1822913721 0.552228276
## [635,] 0.557088374 0.5724626993 -1.7135313522 1.207673719
## [636,] 0.149998204 -0.7640932190 1.1611250713 0.317732140
## [637,] -0.888689303 0.5344050809 -0.0479420797 -0.138812068
## [638,] 0.182436410 -0.7012515988 1.1959956482 0.306905627
## [639,] 0.292515584 -0.4948547042 -0.7288114561 -2.058599349
## [640,] 0.384432832 -1.1165091774 -2.6955386055 0.642450851
## [641,] -1.008099402 0.1177567890 -0.2852685068 -0.184174676
## [642,] -0.972663098 0.3487604828 -0.1517151727 -0.121345131
## [643,] -1.018134881 0.7856493007 0.1080777947 0.135237798
## [644,] -0.129741415 -1.4945477152 0.7495627788 0.324407312
## [645,] -0.856803991 0.8204803841 0.1182194599 -0.046309928
## [646,] 0.528400872 -0.5148818937 1.2834067033 -0.031059397
## [647,] -1.003152277 0.0629866024 -0.3177889479 -0.215418357
## [648,] -0.718431729 0.8503547364 0.1269178881 -0.202022016
## [649,] -0.913337412 0.5849218563 -0.0166600920 -0.085398616
## [650,] 0.085370444 -2.1181645613 0.3691080939 -0.225780251
## [651,] -0.972438860 0.3208897639 -0.1681167914 -0.134435778
## [652,] -0.095994593 -1.2080705149 0.9158413376 0.414814671
## [653,] 0.932975224 0.7094543375 -1.6570707304 0.810360028
## [654,] -0.912581690 1.0317911193 0.2460388526 0.119163907
## [655,] -0.856828781 -0.7988345942 -0.8338935611 -0.790903964
## [656,] 1.150931821 0.6804485484 1.9463377286 -0.243745737
## [657,] -0.987157412 0.1222781315 -0.2839520407 -0.207740967
## [658,] -1.024511943 0.7284342401 0.0748454868 0.116737370
## [659,] -0.014020532 -0.9670193932 1.0523201521 0.425274679
## [660,] -0.761561598 -1.2249726642 -1.0905562646 -1.103522298
## [661,] 0.741663353 -1.0069974816 -2.6540399679 0.255347188
## [662,] 1.476918676 -1.3659175755 -0.8730815910 1.515526666
## [663,] -1.028858569 -1.3480124243 -1.1457719968 -0.832771220
## [664,] -1.022696720 -0.1087478006 -0.4175118499 -0.270454600
## [665,] -1.049049623 -0.3936286656 -0.5833256084 -0.369182430
## [666,] 2.482590756 0.1913237442 -0.0219082027 1.000069775
## [667,] -1.025419786 -0.2210122323 -0.4833458882 -0.318743535
## [668,] -0.361657574 0.5365138702 -0.0804744001 -0.783240892
## [669,] -1.040949274 -0.2802032871 -0.5171535406 -0.326944621
## [670,] -1.034501597 -0.5021642958 -0.6480739424 -0.436906748
## [671,] 1.777909122 -0.4633602706 -0.3616891289 1.561967520
## [672,] 0.575960104 0.8278092592 -1.5646035940 1.301981901
## [673,] -1.050928035 -0.4498724749 -0.6162751199 -0.392745247
## [674,] -0.905307677 0.9775233041 0.2136646856 0.085301749
## [675,] 0.597246238 0.8603240333 -1.5468497792 1.290866650
## [676,] -0.678750309 0.2447009992 -0.2317333654 -0.529118830
## [677,] -0.853207174 -1.1330822729 -1.0306544763 -0.949039115
## [678,] -0.698449416 2.8090080902 1.2772740678 0.674173273
## [679,] 1.448480112 -1.7070869943 -1.0718578891 1.393469238
## [680,] 0.249972874 -1.5242445278 0.7077697138 -0.154243300
## [681,] 0.262235704 0.0418743610 1.6278206191 0.550902494
## [682,] -0.110195557 -1.4903277955 0.7507914806 0.302412107
## [683,] 1.991958015 0.4711569300 1.7693867405 -1.369899663
## [684,] -0.612122816 1.5433658179 0.5275778906 -0.013533383
## [685,] 1.593931448 -0.8381103369 -0.5702430064 1.614940254
## [686,] -0.830295788 0.9378799892 0.1855486917 -0.024786714
## [687,] -0.990206217 -0.2134096785 -0.4811322747 -0.358369817
## [688,] 0.286865320 0.2705449081 1.7606946177 0.625892943
## [689,] -0.952459927 -0.0377455255 -0.3802651588 -0.323816348
## [690,] 0.088150689 -0.1073868437 1.5512143381 0.695449364
## [691,] 1.546048265 -0.6809334511 -0.4747587744 1.745853671
## [692,] -0.442495047 0.4632229249 -0.1183874766 -0.717950062
## [693,] -1.103167049 -1.1870482139 -1.0463675823 -0.667756051
## [694,] -1.003049274 0.0630088408 -0.3177824728 -0.215534269
## [695,] 0.610906330 0.2846665856 1.7482332202 0.235568806
## [696,] -0.994346913 0.4557555074 -0.0874154123 -0.045590818
## [697,] -0.855427766 1.2674836128 0.3809574109 0.157554335
## [698,] 1.678284518 -0.5965455906 -0.4336146414 1.622723132
## [699,] 1.387203810 -1.3852868731 -0.8787212930 1.616483960
## [700,] -1.017112014 -0.2750568606 -0.5156550705 -0.353768996
## [701,] -1.047688710 -0.3374965837 -0.5504086282 -0.345037265
## [702,] 2.591000816 1.1639797750 0.5430410319 1.314577051
## [703,] 0.141071518 -1.0452117911 0.9964067687 0.199394362
## [704,] -0.958409837 0.4635142652 -0.0851563174 -0.086031273
## [705,] -0.070208481 -1.2583415972 0.8846308877 0.360120609
## [706,] -0.957976849 0.1844164318 -0.2492862474 -0.214901612
## [707,] -1.019922772 0.0035276162 -0.3516746131 -0.222222922
## [708,] 1.040582830 -0.0946382622 0.7000179410 1.084707607
## [709,] -0.933328740 0.1338996565 -0.2805682351 -0.268315064
## [710,] 0.152449418 -1.3777848985 0.8001334335 0.032530955
## [711,] 0.814167311 0.4046125825 -1.8286964431 0.815673010
## [712,] -0.195145312 0.5470983840 -0.8825814068 0.567452960
plot(Temp2_pca)
#get the original value of the data based on PCA
center <- Temp2_pca$center
scale <- Temp2_pca$scale
new_tita <- as.matrix(Temp2[,-1])
new_tita
## Sex Age Fare Embarked
## [1,] 1 22.00 7.2500 3
## [2,] 2 38.00 71.2833 1
## [3,] 2 26.00 7.9250 3
## [4,] 2 35.00 53.1000 3
## [5,] 1 35.00 8.0500 3
## [6,] 1 54.00 51.8625 3
## [7,] 1 2.00 21.0750 3
## [8,] 2 27.00 11.1333 3
## [9,] 2 14.00 30.0708 1
## [10,] 2 4.00 16.7000 3
## [11,] 2 58.00 26.5500 3
## [12,] 1 20.00 8.0500 3
## [13,] 1 39.00 31.2750 3
## [14,] 2 14.00 7.8542 3
## [15,] 2 55.00 16.0000 3
## [16,] 1 2.00 29.1250 2
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## [537,] 1 36.00 512.3292 1
## [538,] 1 27.00 76.7292 1
## [539,] 1 20.00 9.2250 3
## [540,] 1 14.00 46.9000 3
## [541,] 1 60.00 39.0000 3
## [542,] 1 25.00 41.5792 1
## [543,] 1 14.00 39.6875 3
## [544,] 1 19.00 10.1708 3
## [545,] 1 18.00 7.7958 3
## [546,] 2 15.00 211.3375 3
## [547,] 1 31.00 57.0000 3
## [548,] 2 4.00 13.4167 1
## [549,] 1 25.00 7.2250 1
## [550,] 1 60.00 26.5500 3
## [551,] 1 52.00 13.5000 3
## [552,] 1 44.00 8.0500 3
## [553,] 1 49.00 110.8833 1
## [554,] 1 42.00 7.6500 3
## [555,] 2 18.00 227.5250 1
## [556,] 1 35.00 26.2875 3
## [557,] 2 18.00 14.4542 1
## [558,] 1 25.00 7.7417 2
## [559,] 1 26.00 7.8542 3
## [560,] 1 39.00 26.0000 3
## [561,] 2 45.00 13.5000 3
## [562,] 1 42.00 26.2875 3
## [563,] 2 22.00 151.5500 3
## [564,] 2 24.00 49.5042 1
## [565,] 1 48.00 52.0000 3
## [566,] 1 29.00 9.4833 3
## [567,] 1 52.00 13.0000 3
## [568,] 1 19.00 7.6500 3
## [569,] 2 38.00 227.5250 1
## [570,] 2 27.00 10.5000 3
## [571,] 1 33.00 7.7750 3
## [572,] 2 6.00 33.0000 3
## [573,] 1 17.00 7.0542 3
## [574,] 1 34.00 13.0000 3
## [575,] 1 50.00 13.0000 3
## [576,] 1 27.00 53.1000 3
## [577,] 1 20.00 8.6625 3
## [578,] 2 30.00 21.0000 3
## [579,] 1 25.00 26.0000 3
## [580,] 2 25.00 7.9250 3
## [581,] 2 29.00 211.3375 3
## [582,] 1 11.00 18.7875 1
## [583,] 1 23.00 13.0000 3
## [584,] 1 23.00 13.0000 3
## [585,] 1 28.50 16.1000 3
## [586,] 2 48.00 34.3750 3
## [587,] 1 35.00 512.3292 1
## [588,] 1 36.00 78.8500 3
## [589,] 2 21.00 262.3750 1
## [590,] 1 24.00 16.1000 3
## [591,] 1 31.00 7.9250 3
## [592,] 1 70.00 71.0000 3
## [593,] 1 16.00 20.2500 3
## [594,] 2 30.00 13.0000 3
## [595,] 1 19.00 53.1000 3
## [596,] 1 31.00 7.7500 2
## [597,] 2 4.00 23.0000 3
## [598,] 1 6.00 12.4750 3
## [599,] 1 33.00 9.5000 3
## [600,] 1 23.00 7.8958 3
## [601,] 2 48.00 65.0000 3
## [602,] 1 0.67 14.5000 3
## [603,] 1 28.00 7.7958 3
## [604,] 1 18.00 11.5000 3
## [605,] 1 34.00 8.0500 3
## [606,] 2 33.00 86.5000 3
## [607,] 1 41.00 7.1250 3
## [608,] 1 20.00 7.2292 1
## [609,] 2 36.00 120.0000 3
## [610,] 1 16.00 7.7750 3
## [611,] 2 51.00 77.9583 3
## [612,] 2 30.50 7.7500 2
## [613,] 1 32.00 8.3625 3
## [614,] 1 24.00 9.5000 3
## [615,] 1 48.00 7.8542 3
## [616,] 2 57.00 10.5000 3
## [617,] 2 54.00 23.0000 3
## [618,] 1 18.00 7.7500 3
## [619,] 2 5.00 12.4750 3
## [620,] 2 43.00 211.3375 3
## [621,] 2 13.00 7.2292 1
## [622,] 2 17.00 57.0000 3
## [623,] 1 29.00 30.0000 3
## [624,] 1 25.00 7.0500 3
## [625,] 1 25.00 7.2500 3
## [626,] 2 18.00 7.4958 3
## [627,] 1 8.00 29.1250 2
## [628,] 1 1.00 20.5750 3
## [629,] 1 46.00 79.2000 1
## [630,] 1 16.00 26.0000 3
## [631,] 1 25.00 7.8958 3
## [632,] 1 39.00 13.0000 3
## [633,] 2 49.00 25.9292 3
## [634,] 2 31.00 8.6833 3
## [635,] 1 30.00 7.2292 1
## [636,] 2 30.00 24.1500 3
## [637,] 1 34.00 13.0000 3
## [638,] 2 31.00 26.2500 3
## [639,] 1 11.00 120.0000 3
## [640,] 1 0.42 8.5167 1
## [641,] 1 27.00 6.9750 3
## [642,] 1 31.00 7.7750 3
## [643,] 1 39.00 0.0000 3
## [644,] 2 18.00 7.7750 3
## [645,] 1 39.00 13.0000 3
## [646,] 2 33.00 53.1000 3
## [647,] 1 26.00 7.8875 3
## [648,] 1 39.00 24.1500 3
## [649,] 1 35.00 10.5000 3
## [650,] 2 6.00 31.2750 3
## [651,] 1 30.50 8.0500 3
## [652,] 2 23.00 7.9250 3
## [653,] 1 31.00 37.0042 1
## [654,] 1 43.00 6.4500 3
## [655,] 1 10.00 27.9000 3
## [656,] 2 52.00 93.5000 3
## [657,] 1 27.00 8.6625 3
## [658,] 1 38.00 0.0000 3
## [659,] 2 27.00 12.4750 3
## [660,] 1 2.00 39.6875 3
## [661,] 1 1.00 37.0042 1
## [662,] 2 15.00 14.4542 1
## [663,] 1 0.83 18.7500 3
## [664,] 1 23.00 7.8542 3
## [665,] 1 18.00 8.3000 3
## [666,] 2 39.00 83.1583 1
## [667,] 1 21.00 8.6625 3
## [668,] 1 32.00 56.4958 3
## [669,] 1 20.00 7.9250 3
## [670,] 1 16.00 10.5000 3
## [671,] 2 30.00 31.0000 1
## [672,] 1 34.50 6.4375 1
## [673,] 1 17.00 8.6625 3
## [674,] 1 42.00 7.5500 3
## [675,] 1 35.00 7.8958 1
## [676,] 1 28.00 33.0000 3
## [677,] 1 4.00 31.2750 3
## [678,] 1 74.00 7.7750 3
## [679,] 2 9.00 15.2458 1
## [680,] 2 16.00 39.4000 3
## [681,] 2 44.00 26.0000 3
## [682,] 2 18.00 9.3500 3
## [683,] 2 45.00 164.8667 3
## [684,] 1 51.00 26.5500 3
## [685,] 2 24.00 19.2583 1
## [686,] 1 41.00 14.1083 3
## [687,] 1 21.00 11.5000 3
## [688,] 2 48.00 25.9292 3
## [689,] 1 24.00 13.0000 3
## [690,] 2 42.00 13.0000 3
## [691,] 2 27.00 13.8583 1
## [692,] 1 31.00 50.4958 3
## [693,] 1 4.00 11.1333 3
## [694,] 1 26.00 7.8958 3
## [695,] 2 47.00 52.5542 3
## [696,] 1 33.00 5.0000 3
## [697,] 1 47.00 9.0000 3
## [698,] 2 28.00 24.0000 1
## [699,] 2 15.00 7.2250 1
## [700,] 1 20.00 9.8458 3
## [701,] 1 19.00 7.8958 3
## [702,] 2 56.00 83.1583 1
## [703,] 2 25.00 26.0000 3
## [704,] 1 33.00 7.8958 3
## [705,] 2 22.00 10.5167 3
## [706,] 1 28.00 10.5000 3
## [707,] 1 25.00 7.0500 3
## [708,] 2 39.00 29.1250 2
## [709,] 1 27.00 13.0000 3
## [710,] 2 19.00 30.0000 3
## [711,] 1 26.00 30.0000 1
## [712,] 1 32.00 7.7500 2
#drop(scale(new_tita,center=center, scale=scale)%*%Temp2_pca$rotation[,1])
predict(Temp2_pca)[,1]
## [1] -1.036571945 2.328844131 -0.076863406 0.541154997 -0.943742080
## [6] -0.278861772 -0.992543997 -0.030671121 1.664344689 -0.108260428
## [11] 0.358340114 -1.039398015 -0.630009991 -0.154266787 0.208282705
## [16] -0.121191971 0.080053345 -0.720981351 -0.888689303 0.625733012
## [21] -0.647725138 -0.028458129 0.290832573 2.118171868 0.875161156
## [26] -0.715648479 1.474364633 -0.353680136 -1.033020953 -0.002848466
## [31] 1.430674269 0.031651073 0.091775301 1.737017034 0.649379751
## [36] -0.005330479 -0.729676286 -1.036123470 2.466575808 0.166579768
## [41] 1.459736803 -0.076792792 0.547522780 0.035247891 -0.614660418
## [46] 0.506071875 0.056057955 -0.895091155 -0.025776293 -1.044431067
## [51] -0.134256967 -0.993534474 -0.932468599 0.343048387 -0.220781974
## [56] 0.621242869 -0.361657574 -1.012476731 -0.901655367 0.005110655
## [61] -1.014854325 -0.964009855 -0.503768344 -0.102301041 0.066125823
## [66] -0.738211213 3.069503611 -1.013889766 -0.982004454 -1.041827907
## [71] -0.214309508 -0.845699534 -0.800620638 1.158894058 1.209014909
## [76] 0.161234875 -0.727358414 -0.064471655 -0.173778840 -0.948998041
## [81] -0.932539213 -0.990295149 -0.112161487 -0.926524525 -0.321794824
## [86] 1.473730145 -1.026643890 -0.091546650 1.489723682 -1.034572211
## [91] 0.050371589 -0.821294068 3.500861199 0.059862195 -0.220781974
## [96] 0.856496849 0.027568597 0.036664218 0.492096651 -1.025161831
## [101] -0.893312280 0.584492113 -1.051808084 0.138651104 0.166579768
## [106] -0.946082865 0.609453478 0.106324917 -0.371914372 -1.050427438
## [111] 1.411988553 -0.104543417 0.008732262 -0.290457192 -1.009337404
## [116] -0.689606114 -0.997913218 0.142972844 -0.711415758 -0.837672804
## [121] -0.786174026 0.625789110 -0.813012301 -0.828623295 1.363011889
## [126] 0.628437935 -0.975627392 -0.786447467 0.109524253 -1.004548410
## [131] -1.050928035 -0.767938660 -0.954730098 0.292191896 -0.387165823
## [136] -0.462102217 -0.108437846 -0.196474743 -1.034572211 1.014114107
## [141] -1.054582031 1.877062338 -0.914197553 -1.037266068 -0.819925729
## [146] -0.776470582 -0.042176813 -0.650385190 -0.047950783 -0.939278650
## [151] 0.024380066 -0.984345239 -0.122381475 -0.925047347 1.826492899
## [156] 3.390087901 -0.894706997 -0.026636433 -0.970386917 -0.969406870
## [161] 0.655880718 -1.052152140 -0.198422354 -0.866074733 0.675019418
## [166] 0.628645183 0.915856252 -1.026299834 0.142791800 -1.036571945
## [171] -0.914197553 2.805324565 -0.070486344 -0.663931846 2.352736343
## [176] -0.945222724 -1.064906265 -0.933328740 -0.841709082 0.092394215
## [181] -1.010510802 -1.015370410 -1.046137539 -0.990722301 0.918110825
## [186] -0.985417223 -0.723057710 0.080389515 -0.983485098 -0.663587790
## [191] 0.035763975 -1.015370410 -0.904063665 -0.951599786 -1.038123204
## [196] 0.557036252 0.902107564 -0.085101979 -0.008021331 -0.378687788
## [201] -0.599817166 -0.026241670 -0.541975130 -0.875726341 0.171281245
## [206] 1.576021360 0.923765970 7.783122743 0.300498078 -0.858188104
## [211] 0.053228880 -1.011757819 -0.906960350 -0.672282725 -1.010925472
## [216] 1.933332924 1.565398897 -1.107413754 0.162439072 0.880591976
## [221] 1.028205947 0.042129017 -0.089306659 0.133484249 0.015297746
## [226] -0.990811408 -1.046911665 -1.045775078 0.594006912 -0.957632792
## [231] -1.028557523 -0.837672804 0.666907557 0.803320697 2.453348419
## [236] 0.665415513 -0.078138217 -1.015803398 0.515637469 1.552483175
## [241] 4.592488314 -1.145676128 0.619772454 2.661751642 0.765215150
## [246] 2.099692269 2.386934820 4.572763956 0.147448581 -0.990295149
## [251] -0.666862335 -0.077742039 0.134694456 -0.748737987 1.902679142
## [256] 3.126121828 -1.036571945 -0.996672211 0.775010371 0.159170537
## [261] 3.114677909 -0.800431707 0.049888315 0.111388768 2.023443967
## [266] -0.622997025 0.879968183 -0.941426084 -0.255394947 3.132498891
## [271] -0.879971456 -0.539315078 -0.931424410 3.075880674 -0.926951678
## [276] -0.946082865 -0.875935179 -0.026636433 0.075396564 -1.050389038
## [281] -0.891501476 -1.005684998 0.461432438 -0.886514536 -0.970386917
## [286] 0.481832316 0.062642440 -0.665516910 0.805013470 1.668230548
## [291] -0.956152148 -0.985555446 2.518366521 2.214952369 1.123523486
## [296] -1.071439868 -1.045775078 2.099575543 -0.060343441 -0.110748452
## [301] 3.072971793 0.453398283 -1.049187846 4.293322569 1.403617766
## [306] -0.964424525 0.527503921 -0.239913161 -0.678431042 0.049888315
## [311] 1.459216011 0.451942143 -1.036175592 -0.989932775 2.754308066
## [316] 0.019280820 -1.029798530 -0.045856727 -0.650833665 -0.989862160
## [321] -0.005471708 -0.919785089 -1.001135641 -0.085169588 -0.891582983
## [326] -0.105973355 -0.789408756 -0.845432102 -1.015020343 -1.036433722
## [331] 1.757783372 -0.887899777 0.279130525 -0.064898808 -0.914197553
## [336] 0.022456956 -0.265500247 -0.984176216 0.016245912 -0.901214683
## [341] 0.160202706 0.102809144 -0.962873267 -0.758795250 0.249481579
## [346] -1.070008516 -0.254264370 1.237470265 0.219497592 0.044721460
## [351] 2.405139675 -0.938845662 0.271715283 -1.021403416 -1.010925472
## [356] -0.001128184 -0.225464960 -0.016118675 -0.720532876 1.472767262
## [361] -0.556725983 -0.692886669 0.811752906 1.694326912 0.558983863
## [366] -0.522843943 0.108142017 -0.631254003 -0.950119142 -0.489330748
## [371] -0.799410430 -0.937020961 -0.580237504 1.445664747 -0.917009726
## [376] 0.213805637 1.519713505 -0.078637400 -0.789408756 -0.994466645
## [381] -1.033211299 -0.175773979 -0.627414543 -0.848086144 0.179719640
## [386] 1.565787300 0.999086522 1.014510286 -0.975627392 -1.012126664
## [391] -1.042949008 -0.537594796 1.343183574 -1.033020953 2.517541600
## [396] 1.699155610 -1.017044405 -1.050928035 0.660530495 0.013916019
## [401] 0.834487097 1.742305211 0.192088017 -0.808745776 -0.399919948
## [406] -0.214276500 -0.711036394 2.283404562 -1.020767426 -0.544917926
## [411] 0.006109019 0.211219205 -0.964786899 1.010636449 -1.028557523
## [416] 2.202001714 -0.140940282 0.108142017 -0.919785089 -0.977452092
## [421] -0.005600916 0.474186563 -0.042202731 0.029386913 -0.650385190
## [426] 2.713938533 1.956478889 0.769672284 0.104501632 0.117255756
## [431] -0.740112539 1.915656287 -0.536046543 0.102809144 -0.801680601
## [436] -0.759753800 1.760541037 -0.771997850 0.506019753 -0.104233166
## [441] -0.541975130 1.999422833 0.896150563 0.104492616 -0.913770400
## [446] -0.920746643 -0.814087664 -1.047688710 0.105460181 -0.965303158
## [451] -0.741156728 0.635827880 -0.709795388 -1.064906265 -0.965730136
## [456] 0.037134190 0.601411438 -0.964424525 0.190711792 2.826659903
## [461] -0.599817166 1.003589877 0.762232253 -0.780967356 1.641562798
## [466] -1.026643890 -0.955221393 2.504787476 -0.877145386 -0.708227227
## [471] -0.737562916 -0.954364257 1.295032960 0.147104525 -0.886348518
## [476] 0.828746136 -0.844289504 -0.977541024 -0.716152542 1.858181219
## [481] 1.818545801 0.295813503 -0.943742080 0.618687125 -0.871315208
## [486] 0.024588903 0.168484098 -0.970730973 0.627619931 -0.346802476
## [491] 0.598958458 -1.035450844 -0.933119902 -0.476736169 0.021367562
## [496] 0.760369327 -1.003049274 -0.384373271 -0.854067028 0.858634719
## [501] 0.062617651 -0.001128184 -0.964424525 -0.743387084 0.412967328
## [506] -1.041827907 2.214952369 0.017978214 1.445664747 1.534375252
## [511] -1.047688710 1.073734558 -0.100648369 0.059201877 -1.028264174
## [516] 0.628989240 -0.201650787 0.826856211 -0.958836989 2.051681755
## [521] 0.710618450 0.620806875 -0.649575756 -0.944242677 -1.040949274
## [526] -0.150634288 -0.946082865 -0.892725581 0.398058344 -0.423827822
## [531] -0.690140229 -0.907820490 -1.055564909 -1.010701235 -0.104093527
## [536] 0.515229071 6.863676311 1.400456943 -1.024816185 -0.595529231
## [541] -0.400223903 0.951488913 -0.685036850 -1.019455804 -1.055306779
## [546] 2.377351952 -0.361777480 1.393895544 0.525150940 -0.554729254
## [551] -0.767697146 -0.886348518 1.964607033 -0.904066670 4.140273072
## [556] -0.717413457 1.496049864 -0.239887753 -1.003565532 -0.695473102
## [561] 0.113486911 -0.672774020 1.680024423 1.969285136 -0.315417761
## [566] -0.964217103 -0.773902181 -1.050739105 4.267814319 -0.038530417
## [571] -0.959908973 0.106777812 -1.070887148 -0.888689303 -0.786656305
## [576] -0.435684996 -1.031796848 0.110906488 -0.784751975 -0.083240468
## [581] 2.466630825 0.579363483 -0.958836989 -0.958836989 -0.885291934
## [586] 0.391678276 6.857299249 -0.058732173 4.591895143 -0.913988715
## [591] -0.970801588 0.060668911 -0.913503430 0.011625941 -0.486701495
## [596] -0.201522375 -0.030076997 -1.073762336 -0.938501605 -1.022180461
## [601] 0.771736622 -1.082621690 -0.991536156 -1.009337404 -0.950119142
## [606] 0.942897157 -0.916959019 0.493317750 1.377765637 -1.068319034
## [611] 0.951681199 0.721112588 -0.958995120 -0.995895167 -0.863270160
## [616] 0.152781454 0.288776122 -1.055875161 -0.154315904 2.555909698
## [621] 1.374501807 0.474767141 -0.709603452 -1.019922772 -1.017440758
## [626] -0.133206306 -0.082929597 -1.005126093 1.552283925 -0.842145536
## [631] -1.009426336 -0.856803991 0.293242383 -0.035567539 0.557088374
## [636] 0.149998204 -0.888689303 0.182436410 0.292515584 0.384432832
## [641] -1.008099402 -0.972663098 -1.018134881 -0.129741415 -0.856803991
## [646] 0.528400872 -1.003152277 -0.718431729 -0.913337412 0.085370444
## [651] -0.972438860 -0.095994593 0.932975224 -0.912581690 -0.856828781
## [656] 1.150931821 -0.987157412 -1.024511943 -0.014020532 -0.761561598
## [661] 0.741663353 1.476918676 -1.028858569 -1.022696720 -1.049049623
## [666] 2.482590756 -1.025419786 -0.361657574 -1.040949274 -1.034501597
## [671] 1.777909122 0.575960104 -1.050928035 -0.905307677 0.597246238
## [676] -0.678750309 -0.853207174 -0.698449416 1.448480112 0.249972874
## [681] 0.262235704 -0.110195557 1.991958015 -0.612122816 1.593931448
## [686] -0.830295788 -0.990206217 0.286865320 -0.952459927 0.088150689
## [691] 1.546048265 -0.442495047 -1.103167049 -1.003049274 0.610906330
## [696] -0.994346913 -0.855427766 1.678284518 1.387203810 -1.017112014
## [701] -1.047688710 2.591000816 0.141071518 -0.958409837 -0.070208481
## [706] -0.957976849 -1.019922772 1.040582830 -0.933328740 0.152449418
## [711] 0.814167311 -0.195145312
#The aboved two gives us the same thing. predict is a good function to know.
Temp2$Survived <- as.factor(Temp2$Survived)
out <- sapply(1:4, function(i){plot(Temp2$Survived,Temp2_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="Survived")})
pairs(Temp2_pca$x[,1:4], ylim = c(-6,4),xlim = c(-6,4),panel=function(x,y,...){text(x,y,Temp2$Survived)})
# Better Ways to Visualize
library(factoextra)
## Warning: package 'factoextra' was built under R version 4.2.2
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.2.2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 4.2.2
library(ggfortify)
## Warning: package 'ggfortify' was built under R version 4.2.2
library(psych)
## Warning: package 'psych' was built under R version 4.2.2
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
##
## The following object is masked from 'package:car':
##
## logit
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.2.2
## corrplot 0.92 loaded
library(devtools)
## Warning: package 'devtools' was built under R version 4.2.2
## Loading required package: usethis
## Warning: package 'usethis' was built under R version 4.2.2
# Correlation
pairs.panels(Temp2[,-1],
gap = 0,
bg = c("red", "blue")[Temp2$Survived],
pch=21)
pairs.panels(Temp2_pca$x,
gap=0,
bg = c("red", "blue")[Temp2$Survived],
pch=21)
fviz_eig(Temp2_pca, addlabels = TRUE)
fviz_pca_var(Temp2_pca,col.var = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
fviz_pca_ind(Temp2_pca, col.ind = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
biplot(Temp2_pca)
autoplot(Temp2_pca,
data = Temp2[,-1],
loadings = TRUE,
labels = Temp2$Survived)
# Different PCA Method.
res.pca <- PCA(Temp2[,-1], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 712 individuals, described by 4 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"
# Visualize and Interpret PCA using these functions
#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.
eig.val <- get_eigenvalue(res.pca)
eig.val
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.3962390 34.90598 34.90598
## Dim.2 1.0834721 27.08680 61.99278
## Dim.3 0.8357525 20.89381 82.88659
## Dim.4 0.6845364 17.11341 100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))
var <- get_pca_var(res.pca)
#var$coord: coordinates of variables to create a scatter plot
#var$cos2: represents the quality of representation for variables on the factor map. It’s calculated as the squared coordinates: var.cos2 = var.coord * var.coord.
#var$contrib: contains the contributions (in percentage) of the variables to the principal components.
#The contribution of a variable (var) to a given principal component is (in percentage) : (var.cos2 * 100) / (total cos2 of the component).
var
## Principal Component Analysis Results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the variables"
## 2 "$cor" "Correlations between variables and dimensions"
## 3 "$cos2" "Cos2 for the variables"
## 4 "$contrib" "contributions of the variables"
# Coordinates
head(var$coord)
## Dim.1 Dim.2 Dim.3 Dim.4
## Sex 0.5266623 -0.5509767 0.58680018 -0.2733442
## Age 0.1092086 0.8631286 0.44030704 -0.2218382
## Fare 0.7762952 0.1476404 0.03775527 0.6116720
## Embarked -0.7101444 -0.1144908 0.54417120 0.4318154
# Cos2: quality on the factore map
head(var$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4
## Sex 0.27737322 0.30357527 0.344334452 0.07471705
## Age 0.01192652 0.74499101 0.193870285 0.04921218
## Fare 0.60263426 0.02179770 0.001425461 0.37414258
## Embarked 0.50430502 0.01310815 0.296122294 0.18646454
# Contributions to the principal components
head(var$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4
## Sex 19.8657409 28.018743 41.2005295 10.914987
## Age 0.8541888 68.759592 23.1970933 7.189126
## Fare 43.1612532 2.011838 0.1705601 54.656349
## Embarked 36.1188170 1.209828 35.4318171 27.239538
#The plot Below is also known as variable correlation plots. It shows the relationships between all variables. It can be interpreted as follow:
#Positively correlated variables are grouped together.
#Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
#The distance between variables and the origin measures the quality of the variables on the factor map.
#Variables that are away from the origin are well represented on the factor map.
# Correlation circle
fviz_pca_var(res.pca, col.var = "black")
# Quality of representation
corrplot(var$cos2, is.corr=FALSE)
# Total cos2 of variables on Dim.1 and Dim.2
#A high cos2 indicates a good representation of the variable on the principal component.
#In this case the variable is positioned close to the circumference of the correlation circle.
#A low cos2 indicates that the variable is not perfectly represented by the PCs.
#In this case the variable is close to the center of the circle.
fviz_cos2(res.pca, choice = "var", axes = 1:2)
fviz_pca_var(res.pca, col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
# Change the transparency by cos2 values
fviz_pca_var(res.pca, alpha.var = "cos2")
corrplot(var$contrib, is.corr=FALSE)
# Contributions of variables to PC1
fviz_contrib(res.pca, choice = "var", axes = 1, top = 10)
# Contributions of variables to PC2
fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)
fviz_pca_var(res.pca, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
)
fviz_pca_var(res.pca, alpha.var = "contrib")
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (nbut not "text")
col.ind = Temp2$Survived, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups"
)
# Graph of Indiviuals
ind <- get_pca_ind(res.pca)
ind
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"
#To get access to the different components, use this:
# Coordinates of individuals
head(ind$coord)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 -1.03730064 -0.1676995 -0.45153271 0.280714448
## 2 2.33048128 0.1023637 -0.06444981 -1.148212825
## 3 -0.07691744 -1.0371539 1.01625217 -0.470646581
## 4 0.54153542 -0.4007333 1.35082026 -0.005945636
## 5 -0.94440552 0.5787641 -0.01858446 0.051219834
## 6 -0.27905781 1.7840844 0.64747666 0.311745469
# Quality of individuals
head(ind$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 0.775882656 0.020279178 0.1470161970 5.682197e-02
## 2 0.802928484 0.001549094 0.0006140855 1.949083e-01
## 3 0.002532788 0.460506403 0.4421322704 9.482854e-02
## 4 0.128702188 0.070476288 0.8008060097 1.551418e-05
## 5 0.725218601 0.272367380 0.0002808354 2.133184e-03
## 6 0.020616435 0.842667072 0.1109873388 2.572915e-02
# Contributions of individuals
head(ind$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 0.1082354509 0.003645573 3.426264e-02 1.616788e-02
## 2 0.5463255028 0.001358296 6.980485e-04 2.705006e-01
## 3 0.0005951273 0.139440423 1.735583e-01 4.544785e-02
## 4 0.0294994538 0.020816758 3.066461e-01 7.253040e-06
## 5 0.0897175219 0.043421563 5.804199e-05 5.382696e-04
## 6 0.0078333692 0.412603659 7.045155e-02 1.993994e-02
fviz_pca_ind(res.pca)
fviz_pca_ind(res.pca, col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_pca_ind(res.pca, pointsize = "cos2",
pointshape = 21, fill = "#E7B800",
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_pca_ind(res.pca, col.ind = "cos2", pointsize = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_cos2(res.pca, choice = "ind")
# Total contribution on PC1 and PC2
fviz_contrib(res.pca, choice = "ind", axes = 1:2)
# Create a random continuous variable of length 23,
# Same length as the number of active individuals in the PCA
set.seed(123)
my.cont.var <- rnorm(49)
# Color individuals by the continuous variable
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (nbut not "text")
col.ind = Temp2$Survived, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups"
)
fviz_pca_ind(res.pca, geom.ind = "point", col.ind = Temp2$Survived,
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, ellipse.type = "confidence",
legend.title = "Groups"
)
fviz_pca_ind(res.pca,
label = "none", # hide individual labels
habillage = Temp2$Survived, # color by groups
addEllipses = TRUE, # Concentration ellipses
palette = "jco"
)
fviz_pca_var(res.pca, geom.var = c("point", "text"))
# Show individuals text labels only
fviz_pca_ind(res.pca, geom.ind = "text")
# Change the size of arrows an labels
fviz_pca_var(res.pca, arrowsize = 1, labelsize = 5,
repel = TRUE)
# Change points size, shape and fill color
# Change labelsize
fviz_pca_ind(res.pca,
pointsize = 3, pointshape = 21, fill = "lightblue",
labelsize = 5, repel = TRUE)
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (but not "text")
group.ind = Temp2$Survived, # color by groups
legend.title = "Groups",
mean.point = FALSE)
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (but not "text")
group.ind = Temp2$Survived, # color by groups
legend.title = "Groups",
mean.point = TRUE)
fviz_pca_var(res.pca, axes.linetype = "blank")
ind.p <- fviz_pca_ind(res.pca, geom = "point", col.ind = Temp2$Survived)
ggpubr::ggpar(ind.p,
title = "Principal Component Analysis",
subtitle = "Iris data set",
caption = "Source: factoextra",
xlab = "PC1", ylab = "PC2",
legend.title = "Survived", legend.position = "top",
ggtheme = theme_gray(), palette = "jco"
)
fviz_pca_biplot(res.pca, repel = TRUE,col.ind = Temp2$Survived,
col.var = "#2E9FDF", # Variables color
)
fviz_pca_biplot(res.pca,
col.ind = Temp2$Survived, palette = "jco",
addEllipses = TRUE, label = "var",
col.var = "black", repel = TRUE,
legend.title = "Survived")
fviz_pca_biplot(res.pca,
# Fill individuals by groups
geom.ind = "point",
pointshape = 21,
pointsize = 2.5,
fill.ind = Temp2$Survived,
col.ind = "black",
# Color variable by groups
legend.title = list(fill = "Survived", color = "Clusters"),
repel = TRUE # Avoid label overplotting
)+
ggpubr::fill_palette("jco")+ # Indiviual fill color
ggpubr::color_palette("npg") # Variable colors
fviz_pca_biplot(res.pca,
# Individuals
geom.ind = "point",
fill.ind = Temp2$Survived, col.ind = "black",
pointshape = 21, pointsize = 2,
palette = "jco",
addEllipses = TRUE,
# Variables
alpha.var ="contrib", col.var = "contrib",
gradient.cols = "RdYlBu",
legend.title = list(fill = "Survived", color = "Contrib",
alpha = "Contrib")
)
## http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/112-pca-principal-component-analysis-essentials/
# ANOVA
Temp2
## # A tibble: 712 × 5
## Survived Sex Age Fare Embarked
## <fct> <dbl> <dbl> <dbl> <dbl>
## 1 0 1 22 7.25 3
## 2 1 2 38 71.3 1
## 3 1 2 26 7.92 3
## 4 1 2 35 53.1 3
## 5 0 1 35 8.05 3
## 6 0 1 54 51.9 3
## 7 0 1 2 21.1 3
## 8 1 2 27 11.1 3
## 9 1 2 14 30.1 1
## 10 1 2 4 16.7 3
## # … with 702 more rows
summary(aov(Sex ~ Age))
## Df Sum Sq Mean Sq F value Pr(>F)
## Age 1 1.62 1.6163 7.033 0.00818 **
## Residuals 710 163.17 0.2298
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Age ~ Fare))
## Df Sum Sq Mean Sq F value Pr(>F)
## Fare 1 1296 1295.6 6.214 0.0129 *
## Residuals 710 148046 208.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Fare ~ Embarked))
## Df Sum Sq Mean Sq F value Pr(>F)
## Embarked 1 160160 160160 62.06 1.25e-14 ***
## Residuals 710 1832418 2581
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(aov(Sex ~ Embarked))
## Df Sum Sq Mean Sq F value Pr(>F)
## Embarked 1 1.98 1.9808 8.639 0.0034 **
## Residuals 710 162.80 0.2293
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# BoxM
library(biotools)
## Warning: package 'biotools' was built under R version 4.2.2
## Loading required package: MASS
##
## Attaching package: 'MASS'
##
## The following object is masked from 'package:dplyr':
##
## select
##
## ---
## biotools version 4.2
boxM(Temp2[,2:5],Survived)
##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: Temp2[, 2:5]
## Chi-Sq (approx.) = 282.92, df = 10, p-value < 2.2e-16
# MANOVA
summary(manova(as.matrix(Temp2[,-1])~ Survived))
## Df Pillai approx F num Df den Df Pr(>F)
## Survived 1 0.32642 85.653 4 707 < 2.2e-16 ***
## Residuals 710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1